In porous bed rivers, geomorphic structures such as boulder steps are known to initiate riverbed mixing of river and groundwater in a process called hyporheic exchange [Harvey and Bencala, 1993; Hester and Doyle, 2008]. Hyporheic exchange has beneficial ecological functions [Boulton et al., 1998; Boulton et al., 2010; O'Connor and Harvey, 2008; Poole, 2010], and is of interest in river restoration design [Crispell and Endreny, 2009; Hester and Doyle, 2008; Kasahara and Hill, 2006; Lautz and Fanelli, 2008]. Hydraulic jumps are characterized by their disruption of the water surface profile and local hydraulics [Chanson, 2009], and hyporheic exchange in rivers is sensitive to local water surface profiles and hydraulics [Buffington and Tonina, 2009; Tonina and Buffington, 2009], yet the influence of hydraulic jumps on hyporheic exchange has gone unexamined.
 The goal of this study is to characterize local flow path patterns of hyporheic exchange at river steps, with and without the rapidly varied flow of hydraulic jumps. Our question is, how do the hyporheic flow paths change when we introduce the rapidly varied flow transitions (i.e., abrupt changes in the water surface profile and velocity field) associated with a hydraulic jump? We addressed our question with flume experiments and separate hydrodynamic model simulations, adjusting discharge rates to remove or introduce a hydraulic jump. We used the laboratory flume experiments to delineate flow path directions and zones, and the hydrodynamic model simulations to quantitatively explore the connections between river geometry, hydraulic jumps, and hyporheic exchange. Because the hyporheic exchange regulates fluxes of water and constituents, we discuss potential implications of this physically based hyporheic research on biogeochemical patterns and the river ecosystem.
1.1. Physical Drivers of Hyporheic Exchange at Steps
 Hyporheic exchange of solute may be regulated by several physical drivers when there is adequate bed form roughness and hydraulic force. These drivers include diffusion, advection, and momentum [Kaser et al., 2009; O'Connor and Harvey, 2008; Packman et al., 2004]; as well as sediment turn-over processes [Elliott and Brooks, 1997b]. In a river system, molecular diffusion is considered to contribute a small component of total exchange [O'Connor and Harvey, 2008] and the turn-over and turbulent momentum processes have a chaotic nature, making them difficult to generalize [Tonina and Buffington, 2009]. Studies of hyporheic exchange at river steps typically focus on the advection driver [Anderson et al., 2005; Buffington and Tonina, 2009; Harvey and Bencala, 1993; Kasahara and Wondzell, 2003; Kaser et al., 2009; Wondzell, 2006]. Advective exchange is driven by hydraulic head, h (m), which is composed of elevation head, z (m); pressure head, (m); and velocity head, u2/2g (m), components; where p is internal pressure (Pa), is density (kg/m3), g is gravitational acceleration, and u is velocity (m/s). Most prior analyses of hyporheic exchange at river steps have predicted fluxes using a hydrostatic water surface profile [Gooseff et al., 2006; Harvey and Bencala, 1993; Kasahara and Wondzell, 2003; Lautz and Siegel, 2006], neglecting hydrodynamic processes and changes in velocity head. The combined elevation head and hydrostatic pressure head are typically referred to as piezometric head. The hydrostatic analysis of exchange assumes the piezometric head can be the dominant hyporheic driver. Laboratory flume research of a riffle-pool sequence has shown, however, that the water surface profile based piezometric head can be a poor predictor of the spatial patterns of exchange along the streambed, due to velocity stagnation and pressure head behaving in a hydrodynamic manner [Tonina and Buffington, 2007]. Hydrodynamic analysis of exchange has not been applied to a river step, but velocity stagnation along riffle-pool sequences of a fixed wavelength and amplitude has been characterized. Elliott and Brooks [1997a] used laboratory flume experiments to establish an analytical pumping model for a repeating bed form (e.g., triangular, riffle pool) which predicts a sinusoidal pattern of exchange due to hydrodynamic pressure oscillations. Cardenas and Wilson  used finite element Reynolds-averaged Navier–Stokes (RANS) simulations of surface water turbulence coupled with a groundwater model to simulate the Elliott and Brooks [1997a] triangular bed forms flume experiment. Their results demonstrated how solution of the RANS equations would predict the fluid turbulence and resulting streambed pressure gradient and advective exchange flow paths [Cardenas and Wilson, 2007]. They did not, however, examine how exchange flow paths responded to hydraulic jumps or impermeable river steps.
1.2. Characteristics of Hydraulic Jumps at Steps
 Hydraulic jumps below river steps have been documented and researched in the Italian Dolomite Mountains [Comiti and Lenzi, 2006; Comiti et al., 2009]; the Colorado Rocky Mountains [Wilcox and Wohl, 2007]; and Californian Sierra Nevada Mountains [Vallé and Pasternack, 2006]. Hydraulic jumps describe the streamwise change from relatively shallow and fast flow to deeper and slower flow. Jumps are hydraulically defined as the transition from supercritical to subcritical flow and are a component of a longer streamwise hydraulic phenomenon known as rapidly varied flow (Figure 1). In the streamwise direction across the step, the rapidly varied flow includes a nappe over the step, supercritical flow (Fr1 > 1) below the step at location 1, and an adverse water surface slope along the jump as it returns to subcritical flow (Fr2 < 1) at location 2 [Hager, 1991]. We distinguish two types of nappes and slopes. There is a clinging nappe, which is nearly vertical and parallel with the step face, and a plunging nappe which has a positive slope with water depth decreasing in the streamwise direction. The hydraulic jump has a negative or adverse slope, with water depth increasing in the streamwise direction. Wilcox and Wohl  note that while subcritical flow is the spatially predominant hydraulic condition in a step-pool channel, a small region of supercritical flow and associated hydraulic jumps are commonly found downstream of steps. Chanson  presents a range of commonly identified jumps in rivers with unregulated flows. It is common to find variation in the hydraulic jump length and height, the number of stationary wave crests, the presence or absence of oscillatory flow and dynamic wave crests, and the rates of air entrainment and effective jump density within rollers along the adverse slope of the jump [Chanson, 2009; Vallé and Pasternack, 2002]. The use of novel pressure sensors in large flume experiments has revealed the dynamic impact of a hydraulic jump on streambed pressure head [Pasternack et al., 2007], but studies have not considered how jump-regulated pressure variations impact hyporheic exchange.