Experimental Modeling of Tsunamis Generated by Pyroclastic Density Currents: The Effects of Particle Size Distribution on Wave Generation

Volcanic tsunamis can expand the radius of hazards posed by a volcano well beyond the reach of the eruption itself; however, their source mechanisms are poorly understood. The tsunamigenic potential of pyroclastic density currents was studied experimentally by releasing a fluidized column of glass beads from a reservoir; the beads then ran down an inclined ramp into a water‐filled flume and generated waves. The effects of the particle size distribution on the generated waves were analyzed by comparing the waves generated by flows comprising different proportions of particles of diameters 63–90 μm and 600–850 μm. The flows comprising higher proportions of large particles travel more slowly down the ramp; however, all the flows impact the water at velocities greater than the shallow water wave speed, gh $\sqrt{gh}$ , where h is the still‐water depth. The entrance of the fluidized flow into the water generates a solitary‐like leading wave followed by a smaller trough and trailing waves. Upon impact, the flow separates into a part advected with the wave crest and a part which turbulently mixes with water and propagates along the bottom of the flume, forming an underwater gravity current. A higher proportion of large particles makes the flows more porous, allowing the water to penetrate through the flows more easily, slightly decreasing the efficiency of the energy transfer. While this affects the celerity of the waves, the results show that, over the studied range of particle size distributions, all the flows can generate waves of similar amplitudes regardless of the particle size distribution.

Deeper understanding of the individual source mechanisms is required in order to study and analyze more complex events. Volcanic tsunami source mechanisms include the entrance of the pyroclastic density currents (PDCs) into the sea, volcano-tectonic earthquakes, underwater eruptions, caldera or flank collapse (Latter, 1981;Paris, 2015). In this study we focus on tsunami generation by PDCs flowing down a slope into the sea. A well-known example of a PDC generated tsunami is the 1883 eruption of Krakatau volcano in Indonesia. The eruption produced massive PDCs that entered the sea and generated large waves, resulting in over 36,000 deaths (Latter, 1981;Self & Rampino, 1981;Verbeek, 1886). More recent volcanic eruptions where PDCs caused tsunamis include the 1994 eruption of the Rabaul volcano (maximum run-up of 8 m, Nishimura et al., 2005), the 1996-1997 and 2003 eruptions of the Soufrière Hills Volcano (maximum run-ups of 4 m on Montserrat and 1 m on Guadeloupe in July 2003, Pelinovsky et al., 2004) and the 2019 eruption of Stromboli volcano (Fornaciai et al., 2019).
Due to limited field observations, the interactions between PDCs and water and the conditions required to generate tsunamis are not well understood and are mainly based on deposit studies, experimental, analytical, and numerical modeling. PDCs are denser-than-air mixtures of volcanic particles, heated air and volcanic gases generated during volcanic eruptions. They can travel up to several tens of kilometres on relatively shallow slopes (i.e., a few degrees) at speeds typically of the order of tens meters per second (Delannay et al., 2017;Druitt, 1998;Freundt et al., 2000;Valentine & Fisher, 2000). Most PDCs are stratified and include a more-dense basal flow zone beneath a turbulent ash cloud that may exchange particles with the denser part (Cas & Wright, 1987;Freundt et al., 2000;Valentine & Fisher, 2000). PDCs are one of the most destructive yet poorly understood volcanic hazards (Dufek, 2016). Tsunamis generated by PDCs are even less well-understood, due to the complexity of the source mechanisms. These mechanisms include the impulsive displacement of water by basal particle-rich flow, dilute ash cloud (cloud pressure and associated shearing), steam explosions, and pressure impulse (Watts & Waythomas, 2003). PDCs generate waves while entering the water and during their propagation underwater, although the latter depends on the water depth, the size and the impact speed of the PDC.
As was seen in Montserrat 1996Montserrat -1997, PDCs separate into two parts upon entering the sea: a dilute part that travels across the water surface, and a dense part that propagates along the bottom of the seafloor as shown in Figure 1 (Cole et al., 1998;Hart et al., 2004). This separation has typically been attributed to the differences in density within the flow. However, numerical simulations, where the PDC was approximated as a Newtonian fluid, show that even PDCs denser than water are capable of shearing the water surface (Battershill et al., 2021). Subaerial and underwater parts of the flow entrain air and water, respectively, by vertical motion of the flow. These two parts can generate water waves separately; however, the dense basal part of the flow is more efficient at producing large and coherent water waves and has received the most attention from the tsunami research community (Bougouin et al., 2020;Walder et al., 2003;Watts & Waythomas, 2003). With particles at temperatures that can reach hundreds of degrees Celsius (Dufek, 2016;Dufek et al., 2007), many PDCs also have large amounts of thermal energy that can be transferred into tsunami. Steam eruptions resulting from interactions of hot pyroclastic material with water may enhance the wave generation process. This paper reports an experimental investigation of PDC generated tsunamis by simulating the entrance of fluidized granular flows into water. The granular flows most closely mimic the basal part of two-layer PDCs, including block and ash flows, generated at composite volcanoes of volcanic arcs. In the following subsections, we present a review of currently existing studies on the modeling of a fluidized granular material and landslide generated waves.

Modeling the Collapse of a Fluidized Material
A remarkable feature of many PDCs is their high mobility, which allows them to travel large distances on relatively shallow slopes. Mechanisms that could be responsible for this high mobility of the PDCs include: generation of air lubrication at the flow base forming an almost frictionless basal region (Kent, 1966;Lube et al., 2019), segregation of small particles forming a rolling layer (Linares-Guerro et al., 2007;Phillips et al., 2006), acoustic fluidization (Collins & Melosh, 2003) and gas-induced fluidization related to pore pressure (Roche, 2012;Wilson, 1980). The pore pressure can occur due to the relative vertical motion of the gas (moving vertically upwards) and the rock particles (flowing vertically downwards). The resulting upward drag force supports the weight of the particles, and hence reduces the basal flow friction allowing the flow to travel large distances on 10.1029/2022JB024847 3 of 23 gentle slopes (Druitt et al., 2007;Lube et al., 2019;Montserrat et al., 2012;Roche 2012;Wilson, 1980). In PDCs the fluidizing gas can be generated during the eruption, ingested at the flow front or released by the particles (Roche et al., 2004;Sparks et al., 1978;Wilson, 1980). Fluidization studies have typically involved dam-break experiments where a granular column in the reservoir is fluidized by introducing an air flux through a porous plate at the base of that reservoir, and released into a horizontal flume by rapidly opening a vertical sluice gate (e.g., Roche et al., 2002;Roche et al., 2004Roche et al., , 2008Rowley et al., 2014). The minimum fluidization velocity of the air through the porous plate is controlled by the basal pore fluid pressure, the height of the column, the hydraulic permeability of the granular material, and the air dynamic viscosity (Druitt et al., 2007;Roche, 2012).
The mobility of a collapsed fluidized material depends on the amount of initial pore pressure and on the pressure diffusion timescale (e.g., Roche et al., 2002Roche et al., , 2004Roche et al., , 2011Sparks et al., 1978;Wilson, 1980). Geldart (1973) classified particles based on the fluidization behavior into four groups as presented in Figure 2. Experiments show that flows of particles made up of group A (fine) remain fluidized for longer compared to flows consisting of particles from groups B and D (coarse), which have higher de-aeration rates (Geldart, 1973;Roche et al., 2002Roche et al., , 2004. Very fine particles from group C are difficult to fluidize because cohesive effects dominate the flow behavior. Fluidized flows travel faster than non-fluidized granular flows, and fluidization increases the flow duration and the runout distance. For example, experiments performed by Roche et al. (2008) show that the duration and the runout distance of fluidized flows were respectively 1.2-1.4 and 1.8-2.2 times greater when compared to non-fluidized flows. Several studies have reported that a high content of fines improves the fluidization of the flow and the pore pressure diffusion timescale (Bruni et al., 2006;Lorences et al., 2003;Wilson, 1980). These fine particles confer smaller hydraulic permeability and hence smaller minimum fluidization velocity and lower pore pressure diffusion rates (Roche, 2012;Roche et al., 2002Roche et al., , 2004. Experiments show that under dam-break conditions, PDCs that mainly consist of fine particles propagate as gravity currents that can be approximated as Newtonian fluids (i.e., exhibiting water-like behavior) for most of their duration (Roche et al., 2008).   Geldart (1973), where ρ p is the density of the particles, ρ g is the fluidizing gas density and d is the diameter of the particles. The blue horizontal lines represent the ranges of particle sizes used in the experiments reported in this paper.

Modeling the Entrance of a Fluidized Flow Into Water
A recent study by Bougouin et al. (2020); Bougouin et al. (2021) modeled wave generation by the entrance of fine-grained fluidized flows into water. A fluidized granular column of glass beads of diameter d = 65 ± 10 μm was released from a reservoir, collapsed onto a fluidizing ramp and ran down into a water-filled flume. The flow impacted the water, created a single vertical granular jet over the water surface and generated a high-amplitude solitary-like leading wave followed by a dispersive train. Some particles from the flow were transported by the leading wave, while the rest of the particles mixed with water generating an underwater gravity current that propagated along the flume floor. The leading wave depends on the mass flux per width and the volume per width of the flow, which proved to be the primary parameters affecting the wave amplitudes. To reflect this relationship (Bougouin et al., 2020), proposed a parameter ζ defined as where u i is the initial velocity of the flow, h f is the thickness of the flow, ρ f is the bulk density of the flow, ρ w is the density of water, h is the still water depth and θ is the impact angle. The dimensionless wave amplitudes η/h scale as γζ 2/7 , where γ is a constant. Bougouin et al. (2020) showed that, for similar impact parameters, fine-grained fluidized flows, fine-grained non-fluidized flows and water flows generated waves of similar amplitudes. However, the fine-grained non-fluidized flows traveled down the subaerial inclined plane more slowly than the fine-grained fluidized flows. This suggests that while it was concluded that the nature of the flow does not have a significant impact on the amplitudes of the generated waves, this conclusion is only valid if the flows have the same initial conditions at the point of entry to the water. Nevertheless, the small particle size of a fluidized granular flow decreases the permeability of the flow and limits the penetration of water into the flow (Bougouin et al., 2020). This in turn, allows for more efficient energy transfer between the flow and the water resulting in waves of higher amplitudes.
Moreover, the size of the particles affects the fluidization of the flows, which is a crucial factor in the mobility of PDCs and could potentially impact the generated waves (Geldart, 1973;Roche et al., 2002Roche et al., , 2004. More fluidized flows travel at higher speeds and can transfer significantly more momentum to the water body at the impact, which results in higher wave amplitudes. Fluidized flows also deform significantly at the impact with water. Although the literature has some useful results for single grain sizes, there are still some unknowns about the effects of the particle size distribution of a fluidized flow on the processes leading to wave generation, and on the generated waves. Furthermore, the generation zone has been often disregarded in experimental modeling and analysis due to the challenges in obtaining robust measurement. The effects of the particle diameter on wave generation have been previously researched in landslide generated tsunami experiments and are reviewed in the following section.

Modeling of Landslide Generated Tsunamis and the Context of This Study
The primary mechanism behind waves generated by two-layer PDCs and subaerial landslides is very similar -the waves are predominantly produced by an impulsive displacement of water by the entrance of the mass flow into the sea. Therefore, review and analysis of studies on subaerial landslide generated tsunamis can be beneficial for modeling PDC generated tsunamis. Previous research has considered landslide models ranging from solid blocks to granular flows moving down an inclined plane, where the landslide motion is either forced mechanically (e.g., Fritz et al., 2004) or caused by gravitational forcing alone (e.g., Freundt, 2003).
After sliding down an inclined plane, the landslide enters a water-filled reservoir and pushes the water away, creating a deep U-shaped shoreline (Di Risio et al., 2009;Freundt, 2003). The entrance of the landslide into the water generates a high-amplitude leading wave followed by a lower-amplitude trough (Di Risio et al., 2009;Freundt, 2003;Mohammed & Fritz, 2012;Walder et al., 2003). Waves are generated by a transfer of momentum from the landslide mass to the water during the impact, the submerging of the landslide and its propagation under the water. Commonly used terminology includes impact (generation) zone, near-field and far-field region ( Figure 1). The impact zone is often defined as the entire region above the moving mass flow where the flow is still influencing the free surface elevation and forcing the waves. The near field is the region beyond the impact zone within which the wave is no longer affected by the flow. The far-field region begins when the kinetic and potential energy of waves reach asymptotic values and dispersive effects become important (Walder et al., 2003;Watts & Waythomas, 2003).
Previous studies have typically investigated various parameters which affect wave generation, including: the landslide mass and density, the thickness, length and width of the landslide, the impact velocity, the grain diameter, the landslide release distance from the shore, the landslide impact angle, and the initial water depth. Experiments have usually been undertaken in a two-dimensional (2D) wave flume (Fritz et al., 2004;McFall et al., 2018;Walder et al., 2003), or in a three-dimensional (3D) wave basin (Di Risio et al., 2009;Mohammed & Fritz, 2012;Panizzo et al., 2005). Heller and Spinneken (2015) investigated the importance of the water body geometry of the models and concluded that, for a given landslide width, landslides with high impact Froude number, thickness and mass can generate as high waves in 3D as in 2D. In contrast, landslides with smaller impact Froude number, thickness and mass generate 3D waves with amplitudes up to 2.7 times smaller in the near field and typically an order of magnitude smaller in the far field when compared to 2D waves (Heller et al., 2016;Heller & Spinneken, 2015). In addition, 3D experiments have shown lower efficiency of the energy transfer between the landslide and the water. Previous studies have reported the efficiency of the energy transfer to be between 1% and 85.7% for 2D experiments (Fritz et al., 2004;Heller, 2008;Huber, 1980;Kamphuis & Bowering, 1970;Law & Brebner, 1968;Walder et al., 2003;Watts & Waythomas, 2003), while only 1%-56.9% of the landslide energy was converted to the wave train for 3D experiments (Bregoli et al., 2017;Heller et al., 2019;Mohammed & Fritz, 2012). This lower energy conversion in 3D studies results from the lack of lateral confinement both of the landslide and the water body. The waves can propagate in all directions, thus more rapidly attenuating the wave amplitudes. These findings suggest that 2D model results should be extrapolated to 3D with caution when using for hazard assessment purposes (Bregoli et al., 2017;Heller et al., 2016). Moreover, given the importance of bathymetry for the dispersive (or at least weakly dispersive) waves generated by a landslide, care should be taken in applying the results of very idealized experiments to more complicated field geometries (Ruffini et al., 2019(Ruffini et al., , 2021. Although Heller and Hager (2010), Lindstrøm (2016) and Robbe-Saule et al. (2021) concluded that the grain size of particles making up a landslide has a negligible effect on the amplitude of the generated waves (for 1 < d < 8 mm), Lee and Huang (2021) showed that wave amplitudes are lower for flows comprising larger particles (for 0.20 < d < 1.29 mm). Granular flows consisting of particles of smaller diameter decrease the flow permeability, which means that water does not penetrate through the flow instantaneously at the impact (Lindstrøm, 2016). In contrast, water can penetrate more easily through flows comprising larger particles, reducing the efficiency of energy transfer and wave generation potential. For a monodisperse column of spherical particles, the flow permeability is defined as where ϵ s is the solid volume fraction and d is the particle diameter (Rhodes, 2008).
This study expands on the work of Bougouin et al. (2020); Bougouin et al. (2021) and explores the effects of the grain size distribution within the flow on the flow-water interactions and the wave generation process. Additionally, we provide detailed information about the hydrodynamics of these interactions and processes. Experiments modeling PDC generated tsunamis were performed by releasing a fluidized granular column from a reservoir, which then ran down the fluidizing ramp into a water-filled flume generating waves. Fluidized flow and wave generation data for this study were collected using high-speed cameras. Section 2 begins by laying out the experimental methodology and data capture process. It then provides detailed information about data processing and extracting quantitative results from the videos. The results of the physical properties of the flowing material before its entry into the water are reported in Section 3.1. In Section 3.2, we analyze the wave generation process, and the velocity field within the flow and the leading wave, calculated using Particle Image Velocimetry (PIV). The results of the properties of the underwater gravity current and the generated waves are presented in Section 3.3. Section 4 includes a discussion of the findings from this study. Finally, Section 5 gives a brief summary and suggests areas for further research.

Experimental Setup and Procedure
Experiments modeling PDC generated tsunamis were conducted by releasing a fluidized granular column from a reservoir which then ran down a fluidizing ramp into a water-filled flume and generated waves. Figure 3 presents the experimental setup and the system of coordinates. The axes are defined such that the x-axis is horizontal aligned with the direction of wave propagation, the y-axis is horizontal aligned with the flume width, and the z-axis is vertical. The origin of the coordinate system (x, y, z) is located at the still water shoreline. The experimental setup consists of a 0.34 m wide, 7.64 m long and 0.50 m high acrylic flume of rectangular cross-section with a maximum water depth of h = 0.25 m.
The flume is connected to a ramp inclined at θ = 13°. The ramp is confined with lateral walls and consists of two parts: a gas-releasing porous, fluidizing ramp and a non-fluidizing submerged ramp. The fluidizing ramp is made of a steel box with a 2 mm thick porous plate on top of it (the maximum diameter of the pores is 30 μm). At the top of the fluidizing ramp, there is a particle reservoir to hold the granular material before its release. The reservoir is opened by a swinging gate at an angular speed of approximately 4 rad/s, so the opening of the gate takes approximately 0.2 s. The gate is connected to a small LED light that switches on when the gate opens. The fluidizing ramp and the reservoir are connected to a compressed air supply to fluidize the granular material and maintain the fluidization during its motion down the fluidizing ramp. This ramp ends at the shoreline (x = 0 m) so that material is actively fluidized until it reaches the water.
All the experiments were performed with a constant mass of the material, m = 20 kg. The granular material used in the experiments was made up of Ballotini glass beads of density ρ p = 2450-2500 kg/m 3 . Two different diameters of the beads were used, d 1 = 63-90 μm (roundness ⩾ 85%) and d 2 = 600-850 μm (roundness ⩾ 65%) corresponding to the A (fine) and D (coarse) groups classified by Geldart (1973) (Figure 2). The corresponding bed height was approximately 0.1 m; however, it varied slightly with the proportion of small beads (see Supporting Information S1 for the images of the granular column in the reservoir). The granular flows made up of these beads were sufficiently permeable for the compressed air to fluidize and expand the mass. We performed a series of experiments with particle size distributions by mass of 100%:0%, 67%:33%, 50%:50% and 33%:67% (small beads:large beads). Hereafter, we will refer to the experiment types by the mass proportion of the small beads. It is important to note that these granular mixtures simulate dense PDCs flowing down a relatively steep slope compared to natural volcanic flanks. While natural PDCs might originate and start flowing down volcanic slopes larger than 13°, the slopes are usually more shallow at the point where they would enter the sea. A notable exception is, however, the Stromboli volcano (Italy) with an average slope of 30° (Lodato et al., 2007). The granular mixtures studied here also do not address dilute PDCs which have much lower particle concentrations.
The experimental procedure was as follows. Pre-dried glass beads were sieved and then thoroughly mixed into size mixtures corresponding to the experiment type. After filling the particle reservoir with the bead mix, the valve supplying the compressed air was opened to fluidize the granular material. Under current experimental conditions, it was not possible to measure or directly control the air velocity. Therefore, all the granular mixtures were fluidized using the same compressed air supply at consistent pressures. Although this raises a question regarding the level of fluidization, multiple experiments were conducted to ensure that the flows were suitably fluidized and repeatable. The minimum velocities required to fluidize the glass beads of diameters 63-90 μm and 600-850 μm are 8.3 × 10 −3 m/s and 2.7 × 10 −1 m/s, respectively (Roche et al., 2002). When the flows comprising 100% small glass beads were released from the reservoir without the compressed air supply, they did not reach the end of the ramp. However, when the flows comprising 100% large glass beads were released from the reservoir with the compressed air supply, they also did not reach the end of the ramp. Therefore, the air velocity used in the reported experiments was at least 8.3 × 10 −3 m/s but less than 2.7 × 10 −1 m/s.
At t = 0 s, the swinging gate was opened, which caused a collapse of the fluidized column onto the ramp. Although the granular columns were thoroughly mixed before each experiment, a size segregation of the glass beads was observed for flows consisting of 33% 63-90 μm particles, with the small beads moving on top of the larger beads (Roche et al., 2005). The particles flowed down the fluidizing ramp and entered the water-filled flume, generating waves. The wave generation process can be divided into three stages: the collapse of the granular column and motion of the flow down the fluidizing ramp; the entrance of the flow into the water and subsequent wave generation; and the propagation of the underwater gravity current and the leading wave in the near-field region. Accordingly, the data were collected and further processed based on these three stages. Due to the flume being only 7.6 m in length, the waves reflected off the end wall of the flume, which prevented the collection of wave data in the far-field region. However, the data collected in the near-field are sufficient to validate near-field results obtained by numerical models or to be used as initial conditions for the wave propagation models, which then can calculate far-field effects.

Data Capture and Processing
All the experimental data were collected using a Phantom VEO 410 high-speed camera. The experiments were recorded at 1,200 × 800 pixels resolution at 1,000 frames per second using a Nikon AF NIKKOR 50 mm f/1.4D lens. The camera field of view was approximately 0.6 × 0.4 m (width × height). The camera recordings were synchronized using the LED light, which switched on when the gate opened and determined the initial time of each experiment. The camera was focused on the near sidewall of the flume, such that all of the measured quantities were captured at the near sidewall. This means that the meniscus effect affects the wave measurements (a maximum error of a couple of millimeters, consistent for all the videos), while any near-wall effects could obscure what is happening in the middle of the flume.
All the videos were processed in MATLAB® using algorithms based on pixel intensity threshold methods and in MATLAB® PIVlab (Thielicke & Sonntag, 2021). Before processing the videos, images were corrected for the lens distortion (the mean projection error calculated using MATLAB® Camera Calibration Toolbox was 0.14 pixels, approximately 0.05 mm).
Prior to collecting the wave generation data, the volume of the particle mixture was estimated by analyzing the videos taken of the fluidized granular column in the reservoir and of the collapse of the column on the fluidizing ramp. The shape of the material in the reservoir and on the fluidizing ramp was approximated by a polygon (see Supporting Information S1 for more details). Based on visual observations, which showed minimal lateral variations in the flow height, a uniform distribution of the material across the width of the ramp was assumed. The average flow volume was calculated using V = A × b, where A is the area of the polygon, and b is the width of the flume. The volume values were then used to calculate the flow bulk density, ρ f = m/V.
The theoretical density of a non-fluidized granular mixture consisting of large and small beads was estimated assuming that the small beads are sufficiently small that they fit around the large beads to the maximum extent.
Since the ratio of the radii is 0.1, the shape of the particles was not taken into account. An optimum proportion of small to large beads was calculated assuming a maximum packing ratio of ideal spheres-a hexagonal close packing (Hudson, 1949). If the proportion of the small beads is less than the optimum, the volume is defined by the volume of the large particles. Otherwise, the volume is estimated by assuming there are two layers: an optimally packed mixture of large and small beads and an optimally packed layer of the remaining small beads (see Supporting Information S1 for detailed calculations). The theoretical density of the non-fluidized mixture was estimated using ρ nf = m/V nf , where V nf is the volume of the non-fluidized mixture.

Flow Kinematics on the Slope
Firstly, we determined the characteristics of the flow at the point where it would enter the water, that is, the characteristics of the wave maker. The camera was located x = 0 m away from the shoreline, and y = 1 m away from the flume sidewall. To achieve a good contrast between the light-colored flow moving down the fluidizing ramp and the ambient air, we placed a black sheet behind the flume and a light box above the flume centerline, illuminating the flow within this plane.
We developed algorithms based on a pixel thresholding approach to detect the flow boundary, estimate its thickness and calculate the vertical profile of the front velocity. To extract the flow boundary at time t, the pixels from image I t are compared with corresponding pixels from a reference frame I 0 obtained at t = 0 s. The pixels from the frame I t are assigned a value of 1 (white) or 0 (black), depending on whether or not the difference between the corresponding pixels exceeds a threshold. All the connected white pixels represent the flow at time t. The binary boundary of the flow was compared with the initial image I t to assess the accuracy of the chosen pixel threshold, and adjustments were made accordingly. The boundary of the flow was used to estimate the thickness of the flow, h f , by calculating the distance from the top edge of the flow to the ramp.
In order to find the velocity profile of the flow prior entering the water, we identified the flow front at a given height above the ramp. The flow front was defined as the most forward point of the flow. These points were tracked frame by frame, giving the position of the flow front as a function of time. A second-degree polynomial fit was found for these data and differentiated to calculate the flow front velocity at this height. Repeating these steps for each height of interest above the ramp gave the velocity profile of the flow front. The front flow velocity, u i , was obtained by averaging the front velocities over the vertical profile.
The flow may be characterized by one of two Froude numbers: a flow Froude number, defined as = ∕ √ , and an impact Froude number, defined as where u s and g are the shallow water wave speed and the gravitational acceleration, respectively. The flow Froude number represents the ratio of inertial over gravitational stresses, while the impact Froude number relates the flow velocity at the entrance into the water with the shallow water wave speed in the constant-depth section of the flume. The impact Froude number also provides information about the relative timescales: the time in which the flow deforms the water surface to the time it takes for this deformation to leave the impact zone.

Flow-Water Interactions and Wave Generation
Secondly, with the camera still located x = 0 m away from the shoreline and y = 1 m away from the flume sidewall, we captured the entrance of the flow into the water. Good contrast between the light-colored flow, the generated waves within the ambient fluid and the background was achieved by placing a white sheet behind the flume, adding a small amount of blue dye into the water and positioning a 500 W halogen lamp beside the flume (Figure 3).
The data collected at the generation zone were analyzed using PIV in PIVlab (Thielicke & Sonntag, 2021) to obtain a velocity field within the flow and the generated leading wave. PIV calculates a velocity field by tracking the motion of particles between frames separated by a known time step. The PIV analysis involves image pre-processing, velocity field calculation, and image post-processing. The images were pre-processed using Contrast Limited Adaptive Histogram Equalization (CLAHE), which optimizes the images based on their most frequent intensities. The regions of interest were selected and the regions that would give non-physical results (e.g., the area below the ramp) were masked. The images were then divided into smaller interrogation areas to find a cross-correlation matrix between the images. This matrix was then used to estimate the average displacement between the interrogation areas. The matrix was found in the frequency domain using a Fast Fourier Transform. The displacement between the interrogation areas was refined with sub-pixel precision using a 2-3-point Gaussian fit. PIVlab then calculated the velocity field based on that displacement and the known time step between two subsequent frames. A maximum speed of 5 m/s was set to remove spurious outliers from the results.
Two-dimensional PIV analysis usually involves a sheet of light illuminating a column of water with seeding particles to highlight a single 2D slice of the 3D features. In our experiments; however, we analyze flows entering the water and track the movement of flow particles based on the color difference between the light-colored flow and dark water, and based on the intensity contrast within the flow itself. This means that the flow is observed at the side wall of the flume and the y-dimension of the velocity vector is not resolved.

Near-Field Propagation of the Underwater Gravity Current and the Leading Wave
Thirdly, the camera was located x = 1.3 m away from the shoreline and y = 1 m away from the flume sidewall to capture the wave propagation in the near-field and the particulate gravity current traveling underwater. The same lighting arrangement was used as for the wave generation zone; however, a second 500 W halogen lamp was positioned to the side of the flume to achieve better contrast between the generated waves and the ambient air ( Figure 3).
We developed algorithms based on a pixel intensity threshold approach to detect the boundary of the underwater gravity current, calculate its thickness and front velocity, extract the free surface elevation and calculate the celerity of the generated waves.
In order to find the boundary of the underwater gravity current at time t, the image was compared with the reference frame at t = 0 s. The procedure was the same as in Section 2.2.1. The propagation of the gravity current underwater is a very turbulent process, and 3D features were observed. For consistency, the boundary was detected on the near sidewall of the flume for all the videos. The front of the gravity current was tracked every 0.1 s, giving the motion of the gravity current front as a function of time. Having these data, the front velocity of the gravity current, u u , was calculated using a forward difference method. The boundary of the gravity current was also used to estimate its thickness, h u , by calculating the distance from the top boundary of the current to the bottom of the flume.
To extract the surface elevation at time t, the pixels from the frame I t were analyzed column by column to find the first pixel that exceeds a threshold in the analyzed column (light-colored background and dark-colored wave). All these pixels form a continuous curve that corresponds to the spatially-varying free surface elevation at time t. By analyzing videos frame by frame, the surface elevation was found as a function of space (within the limited viewing window) and time.
Similarly to the method used to find the velocity of the fluidized flow moving down the ramp (Section 2.2.1), to calculate the wave celerity, c, we identified the leading wave crest and tracked its motion frame by frame using a pixel intensity threshold approach. The celerities were calculated in the same way as described in Section 2.2.1. These values were compared to the shallow water wave speed, u s , and the theoretical celerity of solitary waves, defined as = √ (ℎ + max) , where η max is the maximum wave amplitude (Laitone, 1960).
In order to estimate the efficiency of the wave generation, the kinetic energy of the fluidized flow upon impact was compared to the wave potential energy (Huber, 1980;Kamphuis & Bowering, 1970). The kinetic energy of the fluidized flow was calculated from the flow front velocities obtained in Section 2.2.1 using The potential energy of the waves can be obtained from the surface elevation and the wave celerity. For waves traveling at speeds close to the shallow water limit, it can be assumed that c = c g , where c g is the group velocity. Moreover, for waves propagating at constant velocities dx = cdt holds true. Therefore, the potential energy of the leading wave was calculated from the surface elevation using where b is the width of the flume, ρ w is the density of water, and t 1 and t 2 determine the start and the end of the leading wave (Fritz et al., 2004). Close to the generation zone, the waves are highly nonlinear; however, further away from the source, linear theory can be assumed (Kamphuis & Bowering, 1970;Le Mehaute & Wange, 1996). Therefore, the total energy of the wave was approximated assuming equipartition between the kinetic and the potential wave energy, E wave ≈ 2E pot . Having calculated the potential energy of the waves, the energy transfer between the flow and the water, and hence the efficiency of wave generation was defined as ɛ = E wave /E kin .

Repeatability of the Experiments
The use of a single camera for these experiments necessitated synthesizing the results of multiple experiments with the camera at different positions, which required a high level of experimental repeatability. Figure 4 presents the temporal evolution of the surface elevation measured at x ≃ 1.6 m (in the center of the camera frame in the near-field position) for flows with 100% 63-90 μm beads. The black line represents surface elevation averaged over 10 repeats with 95% confidence intervals shaded in gray. The motion of the flow down the ramp, its entrance into the water and the flow propagation under the water are very turbulent processes; however, the free surface results at x ≃ 1.6 m are highly repeatable (with an average standard deviation of 0.003 m). Thus we conclude that even though the processes leading to the wave generation are variable, the resultant waves are remarkably repeatable, which gives us confidence in our methodology to conduct the experiments and collect the data at various camera positions. Other experiment types were equally repeatable. We refer the reader to Figure 10 and Section 3.3.2 for further discussion of other experiment types as well as features of the generated waves.

Flow Kinematics on the Slope
This section investigates the physical parameters of the flow moving down the fluidizing ramp (Table 1). As the mass of the material was kept constant for all the experiment types, we estimated the flow volume and the bulk density of the flow. The bulk density for flows consisting of 100% and 67% 63-90 μm particles is in the upper range for natural dense PDCs, where ρ PDC = 500-1,500 kg/m 3 (Delannay et al., 2017;Freundt, 2003;Roche, 2012), whereas the densities of flows with 50% and 33% 63-90 μm beads are within 30% of the upper limit. Although the theoretical calculations are based on a number of assumptions (e.g., the particles are perfectly  Note. The first column corresponds to the performed experiment types as referred to in the main text.  (Roche et al., 2005), they follow the same increasing trend. Theoretical calculations of the densities of non-fluidized mixtures also show that the densities are greater for experiments with higher proportions of large beads, for the analyzed range of particle proportions.  (Table 1). The values of the impact Froude number, Fr i , are all significantly larger than 1 at the point where the flow enters the water. An impact Froude number greater than 1 shows that the flow impacts the water at speeds greater than the shallow water wave speed for that water depth. This means that the flow travels faster than the generated wave and it will keep displacing the water, pumping energy into the wave system, until the flow velocity reduces to u s . As long as the flow velocity is larger than u s , the waves will not be able to propagate separately, and will form one big wave system. Although the amplitudes of the generated waves depend on the water depth and the thickness of the flow, an impact Froude number greater than 1 suggests a significant tsunamigenic potential.

Flow-Water Interactions and Wave Generation
The wave generation process at x = 0 m is explored in this section. Figure 6 presents an overview of the wave generation stages. What we observe here is the complex process of the transition of the fluidized granular flow consisting of particles and air into a new underwater flow consisting of particles and water. As discussed in Section 3.1, the impact velocity of the fluidized granular flow, u i , is greater than the shallow water wave speed so the entrance of the flow into the water generates a forced wave which is initially pushed by the flow (Figure 6a). After a short time, the flow transfers much of its kinetic energy to the water column and particles from the flow undergo turbulent mixing, forming a new flow made up of particles and water. We refer to this new underwater flow as an underwater particulate gravity current. Figure 6d shows the temporal evolution of the surface elevation at x = 1.6 m and the underwater gravity current for experiments with 67% 63-90 μm particles. The following subsections focus on the details of the processes in the generation zone, while the properties of the underwater gravity current and the generated waves are discussed in Section 3.3. Figure 7 presents snapshots of the flow impacting the water and generating waves. The superimposed vectors represent velocities within the fluidized flow directly as it impacts the water and the velocities of the flow within the leading wave during and immediately after the generation. The repeatability of the amplitude of the waves generated in the experiments is excellent; however, since these are highly random processes, we observe some variations between the experiment repeats in the generation zone, for example, the shape of the flow underwater and the splashes of water. We refer the reader to Supporting Information S1 for snapshots of the flow entering the water for three repetitions of each experiment type.
While the flow with 100% 63-90 μm particles generates a clean leading wave, the flow behaves like a fluid and displaces the water when entering the flume. The front of the flow pushes the water away, whereas the flow at the back of the wave falls onto the non-fluidizing ramp (Figure 7a). The front of the flow underwater is nearly vertical, pushing the water away instead of piercing through the wave crest and mixing with it. Water cannot easily penetrate and mix with the flow; thus, the energy transfer between the flow and the water increases, and the wave generation is relatively efficient. At t = 0.28 s, there is a clear lift-off of the flow front while propagating down the non-fluidizing ramp. Shortly afterward, we observe a separation of the flow into the part that is advected with the wave crest and the part traveling along the bottom of the ramp (Figures 7b and 7c). The apparent low magnitude velocities within the flow may indicate out-of-plane motion, and hence 3D turbulent mixing with air and water.
When we change the fine particles content, the particles in the top layer of the flow move faster than the particles adjacent to the non-fluidizing ramp and the flow front underwater becomes more inclined (compare e.g., Figure 7b with 7e). A higher proportion of large glass beads makes it easier for water to penetrate through and mix with the flow. Parts of the 67% and 33% 63-90 μm flows pierce through the top of the waves, fall down and mix with water as the waves propagate (Figures 7d and 7e, and Figures 7j and 7k). These turbulent flow-water interactions enhance the wave breaking and splashes of water and flow-water mix resulting in the dissipation of the energy. We also observe similar features as in experiments with 100% 63-90 μm beads: the lift-off of the front of the flow, falling and remixing of the flow at the back of the wave, and the 3D turbulent mixing with air and water. The flows with 67% and 33% 63-90 μm particles also separate into two parts; however, the separation is less pronounced than for flows with 100% 63-90 μm beads (Figures 7e  and 7f, and Figures 7k and 7l).
The wave produced by the flow with 50% 63-90 μm beads also advects a portion of the beads on top of it; however, it seems that the wave crest carries a larger amount of particles than in the experiments with 67% and 33% 63-90 μm particles (compare Figures 7g and 7ure 7j). The wave crest velocity is also significantly greater. Although there is a lift-off of the flow front and remixing at the back of the wave, the separation of the flow is almost absent. The wave breaking takes place much sooner and more violently for the 50% 63-90 μm experiments, dissipating the energy of the wave (Figure 7i).

Propagation of the Underwater Particulate Gravity Current
The propagation of the underwater particulate gravity current and the leading wave in the near-field region is investigated in this section. The wave reaches x ≃ 1.3 m at t ≃ 1 s and enters the camera view as shown in Figure 8 (see Supporting Information S1 for snapshots for three repeats of each experiment type). Although it seems that the flow-water mixing at the generation zone is greater with a higher fraction of the large beads, the wave is carrying particles from the flow that mixed with water in experiments with both 100% and 67% 63-90 μm particles, but not in the others (e.g., Figure 8a, t = 2.5 s and 8b, t = 2.5 s). This could be the result of particles from the flows with 50% and 33% of 63-90 μm particles piercing through the top of the wave, where they fall and mix with water as the wave propagates (Figures 7g -7l).
After the leading wave passes, we observe an underwater particulate gravity current propagating along the flume. The gravity current is undergoing a range of processes; releasing air carried into the flume or entrained upon entrance as bubbles (e.g., Figure 8a, t = 3 s); entraining water in Kelvin-Helmholtz instabilities (e.g., Figure 8c, t = 2.5 s) and depositing material as it propagates underwater. The deposition results in a high-concentration basal layer, the thickness of which decreases as the gravity current propagates (e.g., Figure 8d, t = 3 s). The remaining non-deposited particles of the gravity current consist mainly of small particles still turbulently mixing with water as the mixture propagates along the flume. As a result of this evolution of the gravity current, the deposited gravity current will exhibit a vertical as well as a stream-wise grading (Choux et al., 2004;Roche & Carazzo, 2019;Stix, 2001). The turbulent mixing layer is thinner for experiments with a lower fraction of small particles, which means that the overall gravity current is also thinner (see Table 2).
The underwater gravity current enters the frame only after the leading wave has passed, which means that the gravity current rapidly decelerates to slower than the wave speed. The front velocity of the gravity current seems to have no strong relationship with the particle size distribution as it varies within and across the test types. The variability between repetitions of the same experiment type is at least as large as the variability between different experiment types (see Supporting Information S1 for snapshots for three repeats of each experiment type). However, as shown in Figure 9, the general decreasing trend of velocity as a function of time is consistent across all test types. The gravity current continues to decelerate as it propagates along the flume. 63-90 μm particles. Note that the time t is measured from when the flow entered the water and the time t g (in blue) refers to the time after the gate was opened. We refer the reader to Supporting Information S1 for snapshots for three repeats of each experiment type. Although we treat the processes as uniform across the width of the flume, there are clear 3D features with parts of the underwater gravity current propagating at different velocities (e.g., Figure 8c, t = 3 s). Similar instabilities were observed in previous studies of 3D gravity currents (Inghilesi et al., 2018;Lombardi et al., 2018). The front of the current detaches from the main body and the two parts start traveling at different velocities, forming finger-like structures.
The average velocity of the gravity current underwater over the distance x ∼1.3-1.9 m is approximately 10% of the velocity of the fluidized flow traveling down the fluidizing ramp. This is significantly smaller than the celerity of the generated waves and gives the underwater Fr i between 0.1 and 0.3. Therefore, after the leading wave detaches from the flow, we observe no interactions between the wave and the underwater gravity current. Figure 10 presents the temporal evolution of the surface elevation at a distance x = 1.6 m away from the shore. The entrance of the flow into the water generates a high-amplitude solitary-like leading wave followed by a much smaller trough and trailing waves. The particle size distribution has a very slight effect on the overall wave profiles. In general, flows with higher fractions of large beads have slightly lower wave amplitudes, although the waves generated by flows with 30% 63-90 μm particles have higher amplitudes than experiments with 50% 63-90 μm particles (see Table 2). Flows comprising 67% and 50% 63-90 μm particles also seem to generate waves of less repeatable crest amplitudes, as shown in the insets in Figure 10.

Near-Field Waves and Energy Transfer
While the particle size distribution has a negligible effect on the wave amplitudes, flows with higher proportion of large beads result in waves with lower celerities with the minimum wave celerity calculated for flows having 50% 63-90 μm particles (see Table 2). With the assumption of equipartition of energy, the average energy transfer between the fluidized flow and the water was found to be between 5.3% and 9.8% (Table 2).

Flow Kinematics on the Slope
After being released from the reservoir, the fluidized granular column collapses onto the fluidizing ramp. The flow front velocity profile changes in time, but the average velocities are within the range of the values reported by Bougouin et al. (2020). In the experiments reported here, when the same flows were released from the reservoir without the compressed air supply (non-fluidized flows), they did not reach the end of the ramp and so did not impact the water. While this apparently contradicts the finding of Bougouin et al. (2020), where the fluidized and non-fluidized small-grained flows produced waves of similar amplitudes, those results were comparing similar effective volumes, that is, volumes that entered the water, disregarding the material that stayed on the ramp in the non-fluidized case. Bougouin et al. (2020) used different volumes of granular material, so that large-volume non-fluidized flows could enter the water. The effective volume was therefore in the range 0.003-0.026 m 3 . As the non-fluidized flow does not reach the shoreline in the experiments reported here, the effective volume is zero. Another possible explanation for differences in the results reported here and by Bougouin et al. (2020) might be the differences in the experimental setup, such as the length and width of the fluidizing ramp.
The lower velocities of the flows consisting of higher proportions of large beads might be explained by decreased fluidization rates. Comparing the ratios of V/V nf , the rate of mass expansion is lower for flows with higher proportions of large beads. Since under the reported experimental conditions, all the flows are fluidized using the same air velocity, the fluidization is less effective for flows containing a higher proportion of large beads. This is because the minimum air velocity for fluidizing the large beads is about 30 times larger than for the small particles (Roche et al., 2004). The focus of this study was to explore the effect of particle size distribution on the wave generation under the same initial conditions, that is, the same mass of the flow and the same air velocity available to fluidize the granular material.
Our results confirm the importance of the vertical velocity profile in describing the evolution of the shape of the granular flow front moving down an inclined plane (Hogg & Pritchard, 2004;Saingier et al., 2016). Saingier et al. (2016) demonstrated that for a steady uniform non-fluidized granular flow on an inclined plane with no-slip boundary conditions, the velocity profile follows a Bagnold-like profile in uniform regions (GDR MiDi, 2004). However, their results suggest that the velocity profile of the front of the flow does not follow the Bagnold-like profile, and a non-constant shape factor should be introduced (Hogg & Pritchard, 2004). We observe a more significant change in the shape of the flow front with time for faster and thinner flows, that is, for flows comprising 100% and 67% 63-90 μm beads. Although the flows studied here are both initially fluidized in the reservoir and actively fluidized throughout travel down the ramp, the results qualitatively agree with the work of Saingier et al. (2016) who observed a progressive flattening of the flow front with increased flow Froude number.

Flow-Water Interactions and Wave Generation
The fluidized granular flow impacts the water and generates a nearly vertical granular jet over the water surface ( Figure 6a). Similar features were recorded by Freundt (2003) and Bougouin et al. (2020), who modeled flows consisting of natural volcanic ash and fluidized glass beads, respectively. The PIV analysis has been previously used to obtain the velocity field of the generated waves and the motion of water around the flow (e.g., Zweifel et al., 2006). Performing the PIV analysis based on the color difference between the light-colored flow and the dark water, and based on the intensity contrast within the flow itself, expands this knowledge by providing information about the velocity field within the flow at the impact with water. Moreover, a major advantage of using granular material instead of an analogue fluid is that it allows the dynamics of the particles to be captured as they mix with the water. The most striking result is that the flow separation into the part advected by the wave crest and the part propagating along the non-fluidizing ramp, does not vary significantly with particle size distribution within the flow. However, it is the most pronounced in experiments with 100% 63-90 μm particles. Moreover, particles separating from this monodisperse denser-than-water flow form an upper flow capable of shearing the water surface. This agrees with the numerical modeling of Battershill et al. (2021), which treats the arriving flow as a continuous Newtonian fluid. Battershill et al. (2021) also highlights the importance of the boundary conditions between the flow and the inclined plane on the wave generation. These boundary conditions control the velocity profile of the flows moving down the inclined plane. In this study, we analyze the velocity profile of the flow front traveling down the ramp at the point where it enters the water, and the shape of the flow front as it impacts water. The elongated shape of the front of the flow comprising 100% 63-90 μm particles results in a nearly vertical flow front at the impact with water (e.g., Figure 5a at t = 0.57 s and Figure 7b). On the other hand, the vertical profiles of the front of the flows with higher proportion of large particles create more inclined flow fronts as they impact water (e.g., Figure 5c at t = 0.63 s and Figure 7h). These results suggest that the impact with water and the transition from the fluidizing to non-fluidizing ramp affect all the flows in a similar manner. Specifically, while the whole flow transfers much of its kinetic energy to the water column, there is a greater reduction in the velocity of the particles in the parts of the flow adjacent to the ramp. As the kinetic energy is transferred from the flow to the water column, the flow decelerates. Once its velocity becomes less than the shallow water wave speed (Fr i < 1), the wave is no longer forced and it separates from the flow (see Figures 6b and 6c). The values of Fr i < 1 confirm that the leading wave and the underwater gravity current data were collected in the near-field region.

Near-Field Propagation of the Underwater Particulate Gravity Current and the Leading Wave
The entrance of the flow into the water generates a high-amplitude solitary-like leading wave followed by a much smaller trough and trailing waves. These observations match those recorded in earlier studies (e.g., Bougouin et al., 2020;Di Risio et al., 2009;Freundt, 2003;Mohammed & Fritz, 2012). The generated high-amplitude leading wave resembles a solitary wave, which has a crest height equal to the total wave height (Heller & Hager, 2011;Sander & Hutter, 1991). Zweifel et al. (2006) modeled wave generation by the entrance of a slide moving down a slope inclined at 45° and observed solitary waves for Fr i between 1 and 2.5. Although the flows studied here are flowing down a plane inclined at an angle more than three times smaller, due to the fluidization, their Froude impact numbers are similar. On the other hand, Sarlin et al. (2021) observed solitary waves for 0.35 ≲ Fr i ≲ 0.87. However, these waves were generated by a granular column collapse directly into the water, not by an entrance of a flow moving down an inclined ramp. For the range of analyzed particle size distributions, the smaller the Fr i , (the higher the proportion of large particles) the more the shape of the generated waves resembles solitary waves. Further investigation into wave types classified solitary-like waves as waves usually generated by thick flows, when compared to the water depth, and with large Fr i (Heller & Hager, 2011). While all the fluidized flows studied here have Fr i > 1, they are relatively thin with h f being approximately 20% of the water depth. The wave type clearly depends both on the impact Froude number and the relative thickness of the flow, and the relationship between these parameters and the maximum wave amplitude is not trivial (e.g., Bougouin et al., 2020;Fritz et al., 2004;Heller & Hager, 2010;Zweifel et al., 2006); however, a full discussion of this relationship lies beyond the scope of this study.
Although we are investigating the effect of the particle size distribution, the median grain size of the flow increases with higher proportion of large beads. Therefore, the wave amplitudes are slightly greater for flows with smaller particles, which supports the experimental and numerical results of Lee and Huang (2021). The permeability of flows comprising 100% fine particles is estimated to be in the order of 1.3 × 10 −11 m 2 (Equation 2). While the median particle size increases with higher proportions of large beads, the densities of the flows increase as well, which suggests a higher solid volume fraction. It can be inferred that the fine particle proportion is high enough to fill the spaces between the large beads and, as a result, the permeability of the flow does not significantly change with higher proportions of large beads.
It has to be noted that all the flows in this study were fluidized using the same compressed air supply. The aim of this study was to explore the effect of particle size distribution on the wave generation under the same initial conditions, that is, the same mass and the same air velocity available to fluidize the material. This means that the impact velocity and the thickness of the flow are both dependent on the particle size distribution. However, our results show that even though the particle size distribution affects the impact velocity of the flow and its thickness, which then control the processes in the wave generation zone, all the flows studied here generate waves of similar amplitudes in the near field.
The celerities of the wave crests are within the range of the values reported by Bougouin et al. (2020). Apart from 100% 63-90 μm experiments, all the wave celerities are smaller than the shallow water wave speed for the studied water depth (u s = 1.57 m/s), whereas the solitary wave celerities are on average 20% larger than the measured values (Table 2). Previous studies have demonstrated that the leading wave celerity can be approximated by the shallow water wave theory; however, the approximation of c sol is typically used to assess the celerity of landslide-generated waves for the purpose of hazard modeling (e.g., Bregoli et al., 2017;Fritz et al., 2004;Miller et al., 2017;Mohammed & Fritz, 2012).
Given that the potential energy is a function of wave celerity, wave amplitudes and wave periods, it is not surprising that we observe a similar decreasing pattern of the energy ratio with higher fraction of large beads with the minimum value found for experiments with 50% 63-90 μm particles. The energy ratio was calculated for each repeat separately. The values in Table 2 represent the energy ratio averaged over 10 repeats for each experiment type. It could be argued that the relatively low efficiency of the energy transfer for flows consisting of 67% and 50% 63-90 μm particles is a consequence of more variable wave amplitudes. In addition, the wave energy was obtained using the potential energy of the leading wave without considering the longer-period trough following the crest. The trough is of smaller amplitude than the crest, but it might have contributed to the differences in the wave energy as well. In this study, the energy ratio has been calculated as a ratio between the kinetic energy of the fluidized flow at the impact and the wave energy. These calculations do not consider the potential energy of the flow or the energy dissipation while traveling down the ramp. The numerical modeling of Clous and Abadie (2019) shows that by taking the energy dissipation into account, the calculated energy transfer values could increase and the energy transfer process can be better understood. Moreover, the assumption of equipartition of energy is only strictly valid for the linear wave theory and may overestimate the kinetic energy of the waves (Fritz et al., 2004). Nevertheless, the calculated values provide a reasonable approximation and agree with results reported by the previous studies (e.g., Bregoli et al., 2017;Fritz et al., 2004;Mohammed & Fritz, 2012).

Conclusions
This study was undertaken to investigate the tsunamigenic potential of high-concentration PDCs. Tsunami generation was modeled experimentally by releasing a fluidized column of glass beads from the reservoir which then ran down a fluidizing porous ramp into a water-filled flume and generated waves. The mass of the flow, the air velocity available to fluidize the material and the water depth were kept constant.
After the release from the reservoir, the fluidized granular column collapses and starts propagating down the fluidizing ramp as a relatively thin flow with the kinetic energy dominating the motion ( = ∕ √ > 1, where u i is the impact flow velocity and h f is the flow thickness upon impact). The velocity profile of the flow front traveling down the fluidizing ramp changes in time, which leads to changes in the shape of the flow. The elongation of the front of the flow is more pronounced with flows comprising 100% 63-90 μm particles, whereas the flows with higher proportions of large beads have more uniform velocity profiles. The average flow front velocities are lower for experiments with higher proportions of large beads; however, all the flows impact water at velocities greater than the shallow water wave speed ( = ∕ √ 1, where h is the still water depth).
After entering the flume, the fluidized granular flow displaces water, generating a high-amplitude, forced leading wave (Fr i > 1). The flow decelerates and transfers much of its kinetic energy to the water column and particles from the flow undergo turbulent mixing, forming a new flow made up of particles and water. The flow also separates into a part advected by the wave crest and a part propagating along the bottom of the flume. This flow separation occurs in all experiments but is most pronounced in the experiments using 100% 63-90 μm particles. The fluidized flow emerges from the turbulent mixing zone as an underwater particulate gravity current, which releases air as bubbles, entrains water and deposits the material while propagating along the bottom of the flume. Once the underwater gravity current's velocity is less than that of a shallow water wave (Fr i < 1), the wave detaches from the flow. The front velocity of the current does not seem to be affected by the particle size distribution and slowly decreases with time, with the average velocity over the distance x ∼1.3-1.9 m being approximately 10% of the velocity of the fluidized flow traveling down the fluidizing ramp.
The generated leading wave resembles a solitary wave; however, its celerity is overestimated by the solitary wave theory. The higher the proportion of large beads, the more the shape of the leading wave resembles a solitary wave. Flows with higher proportion of large particles produce waves of slightly lower amplitudes. Although the particle size distribution affects the propagation speed of the waves, the celerities of all the waves are within 14% of the shallow water wave theory. The transfer of the kinetic energy from the fluidized granular flow to the generated waves is slightly more efficient for flows consisting of 100% 63-90 μm particles; this transfer in turn leads to slightly greater wave amplitudes and wave celerities in these experiments.
To conclude, under the same initial conditions (the same flow mass and the same compressed air supply), the particle size distribution results in differences in the flow-water interactions at the generation zone. A higher proportion of large particles makes the flows more permeable, and the water can penetrate through the flows more easily, decreasing the efficiency of the energy transfer. While this affects the celerity of the generated waves, the findings of this study show that over the analyzed range of particle size distributions and with a single, dense, particle density used, the particle size distribution only has a second order effect on the amplitude of the generated waves. A natural progression of this work could be to investigate the effect of the flow mass, density and shape of the particles, as well as the water depth. Further research modeling dilute PDCs or modeling PDCs using natural volcanic material and comparing the results to the idealized experiments reported here would be also very valuable.

Data Availability Statement
The data for this work: a MATLAB script for calculation of the theoretical density of the non-fluidized mixtures, the properties of the granular flows, the water surface profile, the properties of the leading wave, the properties of the underwater gravity current, and the MATLAB script to visualize the data are available at https://doi.org/10.5281/zenodo.6585871.