Turbulent Dynamics of Buoyant Melt Plumes Adjacent Near‐Vertical Glacier Ice

At marine‐terminating glaciers, both buoyant plumes and local currents energize turbulent exchanges that control ice melt. Because of challenges in making centimeter‐scale measurements at glaciers, these dynamics at near‐vertical ice‐ocean boundaries are poorly constrained. Here we present the first observations from instruments robotically bolted to an underwater ice face, and use these to elucidate the interplay between buoyancy and externally forced currents in meltwater plumes. Our observations captured two limiting cases of the flow. When external currents are weak, meltwater buoyancy energizes the turbulence and dominates the near‐boundary stress. When external currents strengthen, the plume diffuses far from the boundary and the associated turbulence decreases. As a result, even relatively weak buoyant melt plumes are as effective as moderate shear flows in delivering heat to the ice. These are the first in‐situ observations to demonstrate how buoyant melt plumes energize near‐boundary turbulence, and why their dynamics are critical in predicting ice melt.


Introduction
Directly quantifying the rate of ice melt at the near-vertical cliffs of marine-terminating glaciers is a challenge due to the boundary's inaccessibility to traditional forms of sampling.The ice-melt process is also complicated because the thermodynamics depend on how local buoyancy production (from melt) combines with the external forcing (temperature T, salinity s, velocity u → ) to control energy flow across the ice boundary.For example, meltwater emerges from the ice as small-scale anomalies in T and s that represent both a source of buoyancy and a source of thermal gradients that control heat flux ( j q ) to the ice (Figure 1a).One challenge is that turbulence theory often assumes an ability to separate the spatial scales of energy sources (large) and sinks (small).In this case, small-scale meltwater anomalies play a role in both buoyant energy production and viscous/thermal dissipation at overlapping (small) spatial scales, violating some traditional assumptions.
At an ice face, we hypothesize that meltwater detaches from the boundary in fine-scale turbulent sweeps, similar to those observed under sea ice (Fer et al., 2004) and in atmospheric boundary layers (Kline et al., 1967), but here also producing buoyant energy at very-small scales.Meltwater buoyancy thus injects additional momentum near the viscous tail of a downscale turbulent energy spectral cascade fueled by large-scale buoyancy forcing from subglacial freshwater plumes (Xu et al., 2013) alongside a zoo of classic ocean- (Gargett, 1989) and fjord-specific near-vertical iceberg face capture turbulent dynamics of buoyant melt plumes and background currents • Buoyant plumes extend 20-50 cm from the boundary and generate broadspectrum temperature and velocity fluctuations that drive horizontal turbulent transports of heat • When ambient horizontal flows are weak, buoyant plumes are the dominant source of boundary layer turbulence that drives heat flux to the ice

Supporting Information:
Supporting Information may be found in the online version of this article.(Bendtsen et al., 2021) turbulence sources.Further complicating the dynamics are energy exchanges as parcels entrain buoyancy from the background stratification as they move vertically against gravity (Kimura et al., 2014;Magorrian & Wells, 2016).
Beneath gently sloping, near-horizontal ice-ocean interfaces, meltwater buoyancy drives along-ice flow.However, this buoyancy also provides static stability, so turbulent exchanges primarily occur through hydrodynamic instability such as Kelvin-Helmholz billows (Smyth, 1999).In 1984, a comprehensive set of observations of turbulent melt dynamics in the Marginal Ice Zone of the Greenland Sea were acquired (McPhee et al., 1987).McPhee et al. (1987) used these data to create an empirical model to predict melt from T, s, and the turbulent stress τ, which formed the basis for the canonical three-equation melt parameterization (Holland & Jenkins, 1999).
Because the stability of the ice permitted detailed, high-accuracy measurements to be obtained, this parameterization (based on ice-melt thermodynamics and three empirical coefficients derived from those experiments), remains the community's primary and only way to predict melt beneath ice shelves (Jenkins et al., 2010) if the relevant flow ( u → , T and s) can be prescribed.
As the ice interface approaches vertical, meltwater can generate sufficient buoyancy to become convectively unstable and directly energize turbulence, as observed in the laboratory by Josberger and Martin (1981).Because the entrainment of warmer ocean water increases with plume buoyancy flux, the melt process creates a positive feedback (Figure 1a) that further energizes the plume to enhance melt.Eckert and Jackson (1950) created a framework for characterizing turbulent free-convection of air adjacent to a heated plate, yielding similarity solutions that were calibrated empirically.While their study remains relevant today (Parker et al., 2021), the icemelt problem is challenging (Cenedese & Straneo, 2023) because (a) melt can be driven by both salinity or thermal gradients, each of which diffuse and influence density in different ways (Gade, 1979;Kerr & McConnochie, 2015); (b) vertical gradients of ocean properties (such as density) affect buoyancy production of turbulent energy and the growth of turbulent plumes (i.e., Magorrian & Wells, 2016); and (c) in addition to buoyancy, other sources of velocity like internal waves (Cusack et al., 2023) or mean currents (Jackson et al., 2020;Zhao et al., 2023) affect shear production of turbulent energy.
Theoretical models (e.g., Wells and Worster (2008)) provide a framework to describe plume evolution, but still require turbulence closure derived from laboratory experiments (McConnochie & Kerr, 2017), numerical simulations (Gayen et al., 2016), or observational analogies (McPhee et al., 1987).At the geophysical scale, empirical models have been developed that assume simplified geometries and turbulence closure.For example, Jenkins (2011) used the framework of MacAyeal (1985) to couple buoyant plume theory with the 3-equation melt model (McPhee et al., 1987) to predict plume evolution.By prescribing an idealized plume geometry, this framework has been used to predict the freshwater distribution from a localized subglacial discharge (Carroll et al., 2016;Cowton et al., 2015) and also for distributed melt (Jackson et al., 2020;Magorrian & Wells, 2016).
To date, there are no experiments analogous to the 1984 sea-ice observations (McPhee et al., 1987) that could be used to constrain the flow and meltrate parameterization for a vertical ice face.In addition to uncertainty in values of drag and transfer coefficients, there is also debate about how to formulate the coupled models themselves.Part of this debate stems from observations of glacier face ablation (Sutherland et al., 2019) and the existence of largescale meltwater intrusions (Jackson et al., 2020) that imply significantly higher meltrates than predicted with the above theories as applied in their commonly used forms.It has been suggested that the boundary layers are energized by external currents which increase the turbulent transfer coefficients (Cusack et al., 2023;Jackson et al., 2020;Slater et al., 2016).Other factors-like energy from exploding air bubbles observed in the laboratory (Wengrove et al., 2023), or ice roughness and channelization observed beneath ice shelves (Stanton et al., 2013;Watkins et al., 2021)-may also be at play here.It is the purpose of this note to describe the first detailed observations of the turbulent flow at a near-vertical glacier-ice face, and to demonstrate how plume buoyancy and external velocities contribute to melt-dynamics.A concurrent paper will extend the analysis of these data to quantify melt rates and assess bias and uncertainty in current melt parameterizations.

The Glacier Meltstake
The Meltstake is a submarine device (Figures 1b-1f) that is remotely bolted to a near-vertical glacier-ice face to directly measure melt and the spatial structure of near-boundary velocity, temperature and turbulence.It is called a "Meltstake" in analogy to the subaerial ablation stakes used by glaciologists to measure ice accumulation and ablation in the field.It is designed to be a stable platform to observe the flow in a reference frame fixed to the ice and in ways that minimize the system's thermal and hydrodynamic impact on melt dynamics.
The body of the Meltstake is suspended outward from the ice on two, 61-cm long carbon fiber tubes, chosen for their mechanical stiffness and low thermal diffusivity, 5 × 10 6 m 2 /s (Macias et al., 2019).Ice screws mounted on the ends of these 16-mm diameter tubes turn using Blue Robotics T200 motors at 23:1 reduction.Each screwassembly rotates within a 25-mm carbon sheath to allow instruments to be rigidly attached at various distances from the ice.A Raspberry Pi "brain" controls drilling power, schedule and underwater communications with a remotely operated vehicle (ROV) through a long-range 28 kHz Delphis Subsea modem.
The Meltstake is transported to the ice face using a BlueRobotics ROV, equipped with a Ping360 imaging sonar and video camera for underwater navigation.The Meltstake is pinned to the ROV and held in place with a Newton linear actuator.The ROV can be deployed from either a robotic vessel equipped with a remotely operated winch or a traditional vessel.High-power Ubiquiti Rocket WiFi allows remote operation of the ROV/Meltstake from several kms away using the standard QGroundControl software.Acoustic messages sent from the ROV trigger drill operations.Once the Meltstake "bites" into the ice, the ROV releases from it.The freed ROV can then monitor the Meltstake, request additional drilling, update the autonomous drilling schedule, or request it to release (by reverse-drilling) and return to the surface.The Meltstake is rated to 100-m depths, ballasted 10 N buoyant, and has a flasher and GPS/satellite beacon for recovery.

Experimental Setting and Measurements
Boundary-layer measurements were made at a freely floating iceberg with 10-m draft, ∼20 km down-fjord from Xeitl Sít' (also called LeConte Glacier) in Southeast Alaska.We deployed the Meltstake on a vertical face of the ice at 6.5-m depth starting at 20:40 UTC, 29 May 2023.As the iceberg melted, we sent acoustic "drill" commands (at 21:39 and 23:05) to advance the Meltstake and move sensors closer to the ice interface.At 23:48 it was released and recovered.At 00:46, May 30 it was again delivered to the same iceberg at 8.5-m depth, drilled further at 01:46, and released at 02:20.
Velocity was imaged with a 5-beam Nortek 1,000 kHz Acoustic Doppler Current Profiler (ADCP) in pulsecoherent mode (4 Hz sampling with 3-4 cm bins).Because of high acoustic backscatter from ice, ADCP data are contaminated by spurious reflections from sidelobes at ranges that exceed the distance of the closest transducer-to-ice distance.We thus attempted to orient the ADCP so that the 4 slant beams encounter the ice at approximately the same range.We use a right-hand coordinate system in which x is along-ice, y is horizontal and positive away from the ice, and z is up.ADCP data were recorded in along-beam coordinates and used for two Between Case 1A and 1B (at 6.5 m depth), the Meltstake was advanced 6 cm further into the ice, placing the thermistor rake within 2 cm of the ice, but also increasing ADCP sidelobe contamination; Case 2 was a separate deployment at 8.5 m depth.Distance from ice (y) was computed acoustically for u and w and using Equation 3 to determine y o for T; note that the ice melted 3-5 mm during each 20-min period, so we treat y independent of time for these plots.
purposes: (a) opposing beams were combined to determine the bulk vertical (w) and along-ice (u) velocities over the 10-70 cm footprint of the spreading beams; (b) along-beam velocities were used to compute (i) the velocity v from the central beam and (ii) turbulent statistics of the flow using the structure function method of Wiles et al. (2006) as implemented by Thomson et al. (2016).Echo backscatter from a Nortek Vector Acoustic Doppler Velocimeter was used to determine meltrate.
Near-boundary temperature was measured using a thermistor "T-rake," a horizontal array of eight, fast-response thermistors, each exposed downward into the expected flow at distances of 2, 4, 7, 12, 23, 39, 58, and 84 mm from the tip of a carbon tube (Figure 1b; Figure S1 in Supporting Information S1).Three fast-response RBR Solos provided additional temperature measurements at 10, 35, and 60 cm from the ice.Salinity profiles were obtained 10-m away from the iceberg using a RBR Concerto CTD deployed from the support vessel, and ranged from 27.4 to 28.4 within the ±1-m depth range around each deployment.

Observations of Buoyancy-and Externally Forced Boundary Layers
Here we examine three time periods that illustrate the range of flow patterns observed (Figure 2).The first two cases represent a boundary layer energized by the vertical rise of buoyant meltwater, which we term "buoyancyforced."The third is an example we term "externally forced," because horizontal velocities were significantly stronger than those of the vertically rising flows.
Case 1A: Quasi-steady buoyant plume.Shortly after the Meltstake was deployed (at 6.5 m depth, and under weak, u ∼ 1 cm/s, crossflow conditions), a quasi-steady plume was observed to flow vertically up the ice at 2-4 cm/s within ∼20 cm of the ice (Figures 2a-2c).During this time, the strongest temperature anomalies (indicative of melt waters) were only observed by sensors within a few millimeters of the T-rake tip, and ∼5 cm from the ice.Case 1B: Strongly undulating buoyant plume.As time evolved the buoyant plume became more variable in time, and weakened slightly in magnitude (Figures 2d-2f).The crossflow remained weak but became slightly unsteady, undulating with similar timescales as the vertical plume.The Meltstake was also advanced toward the ice between 1A and 1B, yielding T observations within 2 cm from the ice.Temperatures most distant from the ice were observed to decrease slightly, and pulses of low-temperature waters were swept 2-10 cm from the ice, contrasting the weaker thermal anomalies in case 1A.Far from the boundary (y > 10 cm), w alternates sign on ∼100 s intervals; these pulses appear correlated with temperature and could be interpreted as turbulent eddies drawing warm ambient fluid toward the boundary.
Case 2: Strong crossflow.After the Meltstake was released and re-drilled into the ice at 8.5-m depth, the iceberg had moved and tidal flows strengthened, exposing the ice to stronger currents (Figures 2g-2i).At this time, u averaged 6 cm/s, w was highly variable but upward (∼1.5 cm/s) on average; both undulated with O(5 min) period.Qualitatively, u and w are out-of-phase (the weakest w generally correspond to the largest u).Temperature anomalies (indicating the presence of meltwater) were observed close to the boundary.

Character of Turbulence in the Buoyant Plume
To glean insight into turbulent dynamics energized by meltwater buoyancy, we examine the undulating plume case (Case 1B) in more detail.We focus on the 5-10 min following drilling (at 23:05) and we look in detail at the 11 individual thermistors in the context of the near-boundary velocities (Figure 3).During the first 5 min, the Trake was in closest proximity to the ice (calculation of y o , the distance from ice to the T-rake's tip, is described in the supplement), such that the innermost thermistor (2 mm from the T-rake tip; midnight blue in Figure 3a) was on average 4 mm from the ice.
These temperature data demonstrate a turbulent melt-and-extrude cycle, whereby the first phase of the eddy draws warm water toward the boundary to initiate melt, and the second phase sweeps the cold meltwaters away from the ice, as also observed in iceberg experiments of Hester et al. (2021).This pattern can be seen in the traces in Figure 3a: at times when T rises at the outer sensors, temperatures at the inner sensors cool.For example, at 23:11, 23:14, and 23:16, the 3 outer sensors (red traces in Figure 3a) warm together, while the inner five sensors (bluegreen traces) cool in unison.These cold pulses-which reached as low as 0°C at times-are the signatures of melt emerging from the boundary.Following these (i.e., at 23:12) are periods in which the temperature of all sensors coalesce together and are the times when warm waters make their closest contact to the ice, presumably temporarily enhancing melt.
Anomalies exceeding ∼1.5°C (below ambient T a ) were detected 25 mm from the boundary, and coherent across all sensors, indicating a pathway for meltwater to be swept out from the laminar sublayer into the outer layer by turbulence.During these events, the ice-perpendicular velocity (Figure 3c) was directed away from the face at approximately 1 cm/s and extended 10s of cm from the boundary.All three velocity components (Figures 3b-3d) varied in concert and with T (Figure 3e).This cycle of perturbations-that brings warm water toward the ice and extrudes cold meltwaters away from the boundary-undulates on ∼100-s periods, and is the signature of a horizontal eddy-transport of heat that fuels melt.

Quantitative Differences in Flow Patterns
To compare the flow characteristics during each of the example time periods, we compute mean profiles of the near-boundary velocity, temperature, turbulent energy and heat transport (Figure 4).Fits of w and T to empirical functions are used to determine spatial scales, magnitudes and gradients, which we use to determine τ and j q , both of which are important parameters to predict melt.Consistency between direct turbulence observations and τ derived from Eckert and Jackson (1950)'s self-similar profiles provides confidence in our interpretations.
Velocity: Eckert and Jackson (1950) derived similarity solutions for the buoyant convection of air adjacent a heated vertical plate, yielding a dimensional vertical velocity w as a function of the nondimensional distance from the wall ŷ = y/δ, where δ is a measure of the boundary layer thickness and assumed to vary slowly in the vertical; 0 < y < δ is also the region over which the solution is valid ( w ≥ 0) and w 1 is a dimensional constant.We use this form to characterize the observed plumes' vertical velocity w(y) by minimizing ∑ (w( y) w( y)) 2 to determine w 1 and δ over 20-min durations.For this solution, the peak velocity is w max = 0.5372w 1 and the plume width, defined by w(L w /δ)/ w max = 1/ e is L w = 0.304δ.As shown in Figure 4b, these fits represent the data well in the region we have observations, and indicate a factor-of-two increase in plume width (L w = 44 cm) during periods of strong crossflow compared to that during weak (L w = 21 22 cm).Because w max decreased for large L w , the total vertical transport per unit width, Q plume = ∫ δ 0 wdy = 0.146w 1 δ, as computed from similarity solution fits, was similar for each case 1A, 1B and 2: 76, 56, and 78 cm 2 /s respectively.
Temperature: T-rake timeseries provide temperature and its gradient with sub-centimeter resolution and at close proximity to the ice boundary.Here we use these and Solo data to characterize the thermal boundary layer (see Supplement for details), which we separate into an outer and inner layer.
We begin by considering Eckert and Jackson (1950)'s similarity solution, for which the characteristic lengthscale for T(y) and w(y) assumed the same (δ).In their form (that set T = 0 at the boundary), a substantial temperature gradient (O ∼ 1°C/m) is predicted far from the boundary, which is not observed here (Figure S2 in Supporting Information S1).Here we modify their form by introducing ΔT to represent the temperature drop in the outer layer: (2) Fits to the outer 5 temperature measurements are roughly consistent with both this form and the logarithmic scaling presented by Tsuji and Nagano (1988) (see Supplement), yielding a 0.2-0.3°Cdrop in the outer boundary layer.Close to the ice, the observed T(y) is inconsistent with Equation 2. Motivated by the early work of Smith (1972) and Tsuji and Nagano (1988), we consider an inner layer shaped by molecular transports and having a different characteristic lengthscale L T , and arbitrarily assume the following exponential form: Here we assume the ice temperature T i = 0°C and solve for T a , the ambient (farfield) temperature, L T , the decay scale, and y o , the distance between ice and T-rake tip, by minimizing for each of the n thermistors.
T a and L T are shown in Figure 4c; y o was 5.4, 1.0, and 13 cm for cases 1A, 1B, and 2 respectively.The meltplumes' thermal lengthscales (L T = 1-4 cm) are a factor of 10 smaller than L w (=20-40 cm); like L w , L T is largest during periods of strong crossflow.The consequences of these differences are evident in the mean temperature profile (Figure 4c and supplement), where two length scales also emerge: one that controls visco-diffusive transports and shapes the inner boundary layer (L T ), and a second that characterizes energetic turbulent transports in the outer boundary layer and diffuses (reduces) larger-scale gradients of T for y > 10 cm.
Turbulence: Of relevance to ice melt is the near-boundary turbulent kinetic energy (TKE), which we compute from along-beam structure functions (Wiles et al., 2006) (Figure 4d).We employ this technique because it does not depend on relationships between acoustic beams, and hence relaxes assumptions of spatial homogeneity.While TKE is relatively uniform in the strong crossflow (red line), it increases toward the boundary (with a maximum at ∼10 cm) for both periods when melt-plume velocities dominated the kinetic energy.This suggests a different source of TKE in each case: shear production during the strong crossflow versus buoyancy production when the external flow weakened.
We calculate the horizontal turbulent heat flux as j q = ρc p K T dT/dy where ρ and c are the density and heat capacity of seawater, K T is the turbulent diffusivity and dT/dy the background temperature gradient.We estimate K T ≈ κu′ℓ, where κ = 0.4 is von Karman's coefficient, u′ ≈

̅̅̅̅̅̅̅̅̅ ̅ TKE
√ , and ℓ is the lengthscale of the energy-containing eddies.In analogy to Perlin et al. (2005), we modify the canonical law-of-the wall scaling (for which ℓ is the distance to the boundary) by limiting the characteristic lengthscale far from the boundary to be that of the plume's eddies, which we approximate as w/(dw/dy).Based on these law-of-the-wall modifications and using Eckert and Jackson (1950)'s model (Equation 1) to estimate plume eddy size, we define ℓ = max(y, w/ (d w/dy)), which increases linearly (ℓ = y) for y < 0.75L w and then decreases almost linearly to 0 at ℓ = 3.3L w .Near the ice, K T increases roughly linearly with distance for all three cases; however, for the strong crossflow, this linear region extends much further away from the boundary.j q is about twice as high for the unsteady plume as the other 2 cases.Note that j q = 1 kW/m 2 is equivalent to 1 cm/hr of ice melt.Eckert and Jackson (1950)'s formulation also provides a convenient way to compute the vertical stress at the ice boundary τ w τ w = 0.0225ρw 2 1 ( where ν is the kinematic viscosity.This estimate of τ w is found to be consistent with laboratory and numerical simulations of turbulent flow from a vertically oriented source of distributed buoyancy (Parker et al., 2021;Zhao et al., 2024).We find τ w which is 0.0098 and 0.0053 Pa for cases 1A and 1B respectively, two to five times larger than τ w = 0.0022 Pa for case 2. For comparison, the stress associated with the horizontal flow (assuming τ u = ρC d u 2 with C d = 2 × 10 3 ) is 0.0072 Pa, similar to that of τ w in the plumes; τ u is roughly 30× smaller during weak crossflow.

Geophysical Research Letters
10.1029/2024GL108790 inferences from farfield observations (Jackson et al., 2020).A remaining challenge is understanding the connections between outer turbulent scales and molecular transports across a real ice interface, that is, the exchanges of buoyancy, heat and momentum fueled by the dynamics sketched in Figure 1a that have until now been largely studied in isolation or under idealized settings.
Our observations of iceberg-scale boundary layers are at higher Reynolds number and have more variability (intrinsic or externally forced) than those simulated in the laboratory (FitzMaurice et al., 2017) or modeled numerically (Gayen et al., 2016).Here, we estimate the rising plumes have 1.5-3.5 m of vertical extent to develop, over which turbulence is observed to extend 20-50 cm from the ice, contrasting the 1-10 cm lateral scales in simulated flows.While the strongest temperature anomalies (a proxy for melt buoyancy) are confined within a 1-4 cm e-folding distance from the ice, the heat transport extends far from the boundary.Qualitatively, this is evidenced by the sweeps in T (Figure 3a), driven by eddies that cyclically advect warm waters toward the boundary and extrude meltwater across the plume on ∼100 s timescales.These eddies are responsible for the turbulent heat flux j q (Figure 4f).

Conclusions
Recent observations of thick meltwater intrusions (Jackson et al., 2020) and unexpectedly high frontal ablation rates (Sutherland et al., 2019) have led to suggestions that Holland and Jenkins (1999) and Jenkins (2011)'s models need to be revisited.Some have suggested transfer coefficients need to be modified (Jackson et al., 2020), others have suggested we need a new empirical model (Schulz et al., 2022), constrained by observations, that is "physically plausible," but not physics based.Neither approach is particularly satisfying because they require arbitrary tuning of coefficients to match observations.The details of the physics are important.
Here we show the ways in which meltwater buoyancy energizes near-boundary turbulence adjacent to a nearvertical section of an iceberg originating from Xeitl Sít' glacier.Importantly, when external sources of mechanical energy are weak, buoyant convection becomes dominant, driving vertical flows that enhance nearboundary turbulence.While these meltwater plumes varied in character, their mean structure was welldescribed by similarity solutions that provide a means of quantifying scales of the flow.
While the character of melt plumes observed here is similar to that predicted by theory (Wells & Worster, 2008), laboratory (Josberger & Martin, 1981) and numerical (Gayen et al., 2016) experiments, the natural flows we observe are more energetic.For example, the turbulent temperature fluctuations observed in laboratory studies of flow adjacent vertical melting ice (Josberger & Martin, 1981) were confined within 2-10 mm of the ice, with fluid outside that layer being quiescent and only occasionally being entrained toward the boundary.In contrast, the boundary layer flows observed here are of larger scale and produce higher heat fluxes.Assessing whether melt rates can be determined from similarity solutions with universal coefficients (at both small and large scales) is our next priority.
In predicting mass loss from open-ocean icebergs, the contribution from buoyant melt plumes is often assumed small compared to melt from horizontal currents (Savage, 2001).Our observations here, and laboratory studies of FitzMaurice et al. ( 2017), span a different part of the parameter space in which buoyant melt plume velocities exceed those of horizontal flows.In this regime (which is likely relevant to many glacier termini), we find that meltwater buoyancy can energize turbulence in the ice-adjacent boundary layer as effectively as a moderate external flow, plausibly driving similar meltrates in both cases.But what sets the TKE, j q and controls the meltrate?While idealized studies provide insight and intuition, all potential factors that influence boundary turbulence must be considered in concert because feedbacks that control melt are nonlinear.Real-world observations are critical to identify the range of dynamics in nature.For example, we have shown that a flow-forced ostensibly by the same external conditions-can have dramatically different character (compare Figure 2 panels a-c with d-f).We hypothesize that the interplay between externally driven turbulence and meltwater convection is critical to the flow dynamics: both shear and buoyant production influence the coherent structures that are of first order importance of turbulent exchange across this boundary layer.Further direct observations that capture the phenomenology of real melt-driven boundary-layers and elucidate the range of dynamical possibilities are critical to inform the next generation of experiments and parameterizations.

Figure 1 .
Figure 1.(a) Cartoon illustrates the interplay between (1) ice morphology (2) turbulent and molecular transports across the ocean-ice interface, and (3) melt-driven buoyant plumes that energize the boundary layer.(b) Meltstake sensors are configured to measure these dynamics with minimal disturbance to the flow.(c) Remotely operated vessel and winched ROV.(d) Meltstake as deployed 12:40 29 May showing ice structure and the sensors' proximity to the interface; the ADCP is outside the frame of view.(e) A Meltstake riding atop the delivery ROV on deck; iceberg from Xeitl Sít' in background.(f) Remote deployment in progress.

Figure 2 .
Figure2.Horizontal, along-ice velocity (a, d, g), vertical velocity (b, e, h), and temperature (c, f, i) within 0.5 m of the ice interface for three twenty-minute periods.Between Case 1A and 1B (at 6.5 m depth), the Meltstake was advanced 6 cm further into the ice, placing the thermistor rake within 2 cm of the ice, but also increasing ADCP sidelobe contamination; Case 2 was a separate deployment at 8.5 m depth.Distance from ice (y) was computed acoustically for u and w and using Equation 3 to determine y o for T; note that the ice melted 3-5 mm during each 20-min period, so we treat y independent of time for these plots.

Figure 3 .
Figure 3. Details of the boundary-layer layer illustrate the dynamics of the unsteady plume: (a) Ten-minute segment of temperature data from the 11 sensors used in Figure 2f.Lower panels show a zoom-in on the first five minutes of that record on 29 May 2023: (b) vertical velocity, (c) ice-normal velocity (positive/red is away from the ice), (c) along-ice velocity, and (d) temperature, plotted against logarithmic distance coordinates to highlight the smallest scales near the ice boundary.In (c), v is from the ADCP center beam so is least-contaminated by acoustic sidelobes and provides unbiased data almost to the ice surface.

Figure 4 .
Figure 4. Mean and turbulent characteristics of the observed boundary layers: (a) along-ice velocity u, (b) vertical velocity w, (c) temperature T, (d) turbulent kinetic energy (TKE), (e) turbulent diffusivity K T , and (f) heat flux j q .Each colored line represents a 20-min average over the time periods shown in Figure 2: steady plume (1A, purple), undulating plume (1B, turquoise), strong crossflow (2, red).Thin/light lines in (a-c) define the central 50% of the data.Gaps in (c) separate data from the temperature rake (∇) and RBR Solos (•), which were separated horizontally by 60 cm and responsible for offsets in T ).Light dashed lines in (b, c) represent Equations 1 and 3 with least-square-fit coefficients as indicated; in (c) fits to Equation 3 use the T-rake data (shown in thick dashed lines) and fits to Equation 2 use the outer 5 T sensors (thin dotted lines).In (d), semi-transparent lines represent estimates of TKE from each of the five individual ADCP beams (heavy lines are the means).