Hyporheic flow path response to hydraulic ... - Wiley Online Library

WATER RESOURCES RESEARCH, VOL. 47, W02517, doi:10.1029/2009WR008631, 2011

Hyporheic flow path response to hydraulic jumps at river steps: Flume and hydrodynamic models T. Endreny,1 L. Lautz,2 and D. I. Siegel2 Received 11 September 2009; revised 18 November 2010; accepted 3 December 2010; published 12 February 2011.

[1] The conceptual model of hyporheic exchange below river steps may oversimplify exchange flow paths if it depicts a uniform pattern of downstream-directed upwelling. This research used nonmobile, porous bed flume experiments and hydrodynamic simulation (CFD) to characterize hyporheic flow paths below a river step with a hydraulic jump. Bed slope was 1%, step height was 4 cm, downstream flow depth was 4 cm, substrate was 1 cm median diameter gravel, and hydraulic jump length was 25 cm in the flume and CFD experiments. With the hydraulic jump, flow paths changed to include downwelling beneath the water plunging into the pool and upstream-directed upwelling at the base of the step and beneath the length of jump. Failure to represent the influence of static and dynamic pressures associated with hydraulic jumps leads to erroneous prediction of subsurface flow paths in 75% of the streambed beneath the jump. A refined conceptual model for hyporheic flow paths below a step with a hydraulic jump includes reversed hyporheic circulation cells, in which downwelling water moves upstream and then upwells, and flow reversals, in which the larger flow net of downstream-directed upwelling encounters a nested flow path of upstream-directed upwelling. Heterogeneity in hyporheic flow paths at hydraulic jumps has the potential to explain field-observed mosaics in streambed redox patterns and expand structure-function relationships used in river management and restoration. Citation: Endreny, T., L. Lautz, and D. I. Siegel (2011), Hyporheic flow path response to hydraulic jumps at river steps: Flume and hydrodynamic models, Water Resour. Res., 47, W02517, doi:10.1029/2009WR008631.

1.

Introduction

[2] 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. [3] 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 1 Department of Environmental Resources Engineering, SUNY School of Environmental Science and Forestry, Syracuse, New York, USA. 2 Department of Earth Sciences, Syracuse University, Syracuse, New York, USA.

Copyright 2011 by the American Geophysical Union. 0043-1397/11/2009WR008631

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 [4] 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].

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ENDRENY ET AL.: HYPORHEIC RESPONSE TO HYDRAULIC JUMPS—FLUME MODEL

Advective exchange is driven by hydraulic head, h (m), which is composed of elevation head, z (m); pressure head, ¼ p=g (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 [2007] 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 [5] 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 [Valle´ 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 [2007] note that while subcritical flow is the spatially predominant hydraulic

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Figure 1. Schematic of rapidly varied flow along a step showing a plunging nappe, an impinging jet, and a hydraulic jump with rollers and a wave. Point 1 along the streambed is associated with supercritical flow and point 2 with subcritical flow. condition in a step-pool channel, a small region of supercritical flow and associated hydraulic jumps are commonly found downstream of steps. Chanson [2009] 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; Valle´ 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.

2.

Methods

2.1. Flume Experiments to Map Exchange Paths [6] Stable bed flume experiments recorded the impact of hydraulic jumps on the subsurface flow paths. This experiment used a subsurface dye tracing technique suited for glass-walled flumes [Packman et al., 2004; Thibodeaux and Boyle, 1987]. Our rectangular flume was 7.5 cm wide, with a slope of 0.01, and 10 mm median diameter substrate was packed 10 cm deep upstream of the step and 6 cm deep downstream of the step. Our flume dimensions and substrate diameter were similar to the Thibodeaux and Boyle [1987] study. Longitudinally, the sediment extended 70 cm upstream of the step, and 180 cm downstream of the step. Two different methods for establishing the step were examined, one obstructing all subsurface flow from upstream to downstream, defined as full penetration ; and the other allowing for subsurface flow paths, defined as partial penetration. Each type of step is common in natural rivers with partially submerged logs and boulders atop gravel as a partial obstruction and bedrock outcrops as a full obstruction [Brierley and Fryirs, 2005; Knighton, 1998; Valle´ and Pasternack, 2006]. Experiments with full or partial obstruction allowed us to examine how the absence or presence of

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advective flows below the step influenced flow paths generated by the hydraulic jump. Steps were constructed from 5 and 10 cm high solid wooden blocks, situated to create a 4 cm vertical drop from the crest of the step to the base of the step and downstream channel bed. In the experiments with 10 cm high steps, the step penetrated the full upstream substrate depth of 10 cm, and was pinned to the metal flume base. In the experiments with 5 cm high steps, the step penetrated half the upstream substrate depth, leaving 5 cm of substrate between the step base and flume base. Clamps were attached to the upper flume walls to compress the walls to the blocks, which reduced the amount of flow between the block and flume wall. The gravel bed upstream and downstream of the step was kept at a constant slope with no pool or scour holes. Substrate depth was limited to a 10 cm maximum due to constraints on the flume wall height. [7] Four experimental runs were completed with the flume, resulting from the combination of partially and fully penetrating step block types and water surface profiles with and without a hydraulic jump. Each of the four runs was repeated 3 times, and for each run the substrate was washed of dye. In the runs without a hydraulic jump, discharge was at 0.4 L/s and flow depth at 1 cm, which kept flow over the step in a clinging nappe and generated no adverse water surface slope downstream of the step. In experimental runs with the hydraulic jump, discharge was 1.2 L/s with a flow depth of 4 cm; a plunging nappe formed over the step, and the jump terminated 30 cm downstream of the step. At both discharges turbulent flow was most prevalent below the nappe, however we only characterize the exchange patterns and not the role of turbulent diffusion in hyporheic exchange [Nagaoka and Ohgaki, 1990]. The change in step, from fully to partially penetrating, did not noticeably change the water surface profile. For each of the four experimental runs, deep blue dye (mixture of FD and C blue 1, red 40) was injected through 0.3 cm diameter flexible tubing into the substrate upstream and downstream of the step. Tubes were either fixed to the interior of the flume, or were inserted with a metal guide to inject dye at new points. Dye injections with the metal guide were used to identify flow path breakpoints. Photographs were taken of the dye as it moved away from the injection points. 2.2. Hydrodynamic Simulation to Quantify Exchange Paths [8] Numerical simulation of the flume step experiments was completed by solving the fully 3D transient conservation of mass and momentum equations in a computational fluid dynamic (CFD) model. The flume water was treated as incompressible, with standard 20 C temperature properties of density and viscosity. Mass continuity was represented according to Hirt and Nichols [1981], @vAy VF @p @uAx @wAz þ þ þ ¼ 0; c2 @t @x @y @z

ð1Þ

where VF is the fractional volume open to flow, c is the speed of sound, t is time, Ai (Ax,Ay, and Az) are the fractional areas open to flow, with subscripts x, y, and z to denote the three flow directions, and ui lim (u, v, and w) x!1 denote the velocities in the x-direction, y-direction, and z-direction. Conservation of momentum and fluid motion

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was represented by the Navier – Stokes equations [Hirt and Nichols, 1981], shown for 1D but valid for three directions (x, y, z), @ui 1 @u @u @u 1 @p þ vAy þ wAz ¼ þ uAx þ fi ; VF @x @y @z @xi @t ð2Þ

where fi (fx, fy, and fz), are the viscous acceleration terms [Hirt and Nichols, 1981]. They are defined as, fi ¼

@ @ @ Ay iy þ ðAz iz Þ wsxi ðAx ix Þ þ @x @y @z

1 ð3Þ VF

where the wsxi (wsx, wsy, and wsz) are the wall shear stresses, which were simulated using law-of-the-wall velocity profiles near the wall; and xi ; yi ; zi are the viscous stresses. Turbulent closure of the momentum equations was achieved using the kinetic energy and dissipation rate transport ðk "Þ two-equation form of the dynamic Renormalization Group method [Yakhot and Orszag, 1986; Yakhot and Smith, 1992]. [9] Implementation of the complete CFD model involved iteratively solving for pressure and velocity at each computational node and time step to simultaneously satisfy the momentum and continuity equations. Equations (1) – (3) apply to surface and subsurface dynamics and were solved using a finite-volume/finite difference method in the commercially available Flow3DV CFD software. Water depth was treated as a free surface boundary and fluid interfaces were treated using the Volume-of-Fluid (VOF) technique, which only requires computation and storage of the volume fraction as one additional variable. [10] Our rectangular model mesh was set to 0.5 cm in the streamwise x direction, 0.1 cm in the vertical z direction, and we used a single 7.5 cm wide cell in the transverse y direction, effectively creating a 2D system. The simulation domain extended 15 cm upstream of the step and 50 cm downstream of the step, and we used a solid cubic block to represent the river step. Time step size was automatically adjusted to maintain stability and ensure fluid fraction advection did not exceed computational cell volumes. No-flow boundary conditions were specified along the model bottom and sides, and free water surface boundaries were established at the upstream and downstream ends. Substrate roughness along the bed was set to 0.4 cm to represent the gravel protrusion length. The porous media component porosity, , was set to 0.3 on the basis of substrate characteristics. Porous media drag coefficients were set to establish permeability of 3.0 106 cm2 and represent a gravel hydraulic conductivity near 0.3 cm/s. This conductivity, K, was determined from dye transport velocities, u, of 1 cm/s where the hydraulic gradient rH, was 1, K ¼ u=rH. In simulations with the hydraulic jump, the free water surface was set to 4 cm, and in simulations without the hydraulic jump, the free water surface was set to 1 cm and roughness was increased to 0.8 cm. This roughness adjustment generated sufficient stabilizing forces to ensure subcritical flow conditions and eliminate surface waves. Upstream of the step, both models had a similar water surface profile and downwelling pattern, indicating that it was hydrodynamics below the step, and not the elevated roughness, that affected our model comparisons. Model simulations were run for the

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fully penetrating and partially penetrating steps, and output included longitudinal and vertical fluxes. [11] In the open channel, the water surface profile was established by maintaining the energy, momentum, and mass balance. When the fluid experienced a rapid change in energy, such as in the drop over a step, the model accounted for friction drag energy losses, and simultaneously conserved mass and momentum by adjusting the fluid velocity and depth. This approach established the convex drawdown profile upstream of the step, and a concave to convex profile downstream of the step. In higher Reynolds number (Re >1000) flows of the open channel the momentum equation considered the turbulent terms. Dye flow patterns showed that turbulence was not observed below the first 1 cm of substrate. In porous media with Darcy flow conditions (Re < 10), the momentum equation reduced to a balance of drag and pressure gradient forces. Analysis of CFD model output was limited to a 25 cm length bounding the step, since it contained the key flow features with and without the jump.

3.

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zone of upstream-directed upwelling (Figures 2c and 2d). Rollers and surface waves along the jump created a pulsating variation in pressure which fragmented the upstreamdirected flux zone. Fragmentation was less common along

Results

3.1. Flume Experiments to Map Exchange Paths [12] Without the hydraulic jump, hyporheic exchange paths below the step were mostly downstream directed. The fully penetrating step created a flow obstruction in the substrate and caused the majority of dye injected upstream of the step to experience upwelling and crest the step in the open channel. Regardless of step penetration depth, the free water surface zone beneath the nappe was turbulent and pulsating. Dye injected at the surface of the streambed beneath the nappe was mixed approximately 0.5 cm into the streambed. With a partially penetrating step, dye injected upstream of the step was characterized by downwelling, and the dye traveled under the step into the downstream section of flume. Downstream of the nappe there was an uninterrupted uniform downstream-directed upwelling zone (Figures 2a and 2b). This downstream-directed upwelling was strong out to 20 cm beyond the step base, and weakened to predominantly horizontal flow at 30 cm. [13] With a hydraulic jump, hyporheic exchange paths upstream of the step were also upwelling with the fully penetrating step and downwelling with the partially penetrating step. At the fully penetrating step, weak flows were observed between the step block and flume walls due to an incomplete seal with the clamps. We characterized four flow path types downstream of the step: downstream-directed upwelling, upstream-directed upwelling, down stream-directed downwelling, and upstream-directed downwelling. Below the step, upstream-directed upwelling and downstream-directed upwelling extended along most of the first 15 cm of downstream streambed. Separating these upwelling zones was a downwelling zone beneath the plunging nappe (Figures 2c and 2d). This zone was about 4 cm in length and had downstream-directed and upstream-directed downwelling components, which extended 2 to 3 cm down into the bed before flow diverged into both upstream-directed and downstream-directed upwelling. When the step was fully penetrating this downwelling zone penetrated 5 cm below the bed, and when the step was partially penetrating the downwelling penetrated only 3 cm and had a shorter upstream extent. Beneath the hydraulic jump, there was a 4 of 10

Figure 2

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the steepest section of the jump. This zone of upstreamdirected upwelling extended 10 cm along the streambed and was equivalent to 2.5 times the flow depth and jump height. The jump terminated about 25 cm from the step base, at which point hyporheic flow was consistently downstream-directed upwelling. [14] We characterized the four hyporheic flow paths and their connectivity with a schematic (Figure 3). We define a reversed hyporheic circulation cell as upstream-directed downwelling connecting to upstream-directed upwelling, which completes a flow cycle for channel water. A reversed hyporheic circulation cell formed beneath the plunging nappe (Figure 3, star). A smaller, shallower, reversed hyporheic circulation cell developed beneath the wave at the end of the jump. This would split the near streambed zone of upstream-directed upwelling. These reversed hyporheic circulation cells only extended 1 to 2 cm upstream and were set within larger flow paths of downstream-directed upwelling. We define a flow reversal as downstream-directed upwelling connecting to upstream-directed upwelling. A flow reversal formed in the bottom 1 cm of porous media beneath the plunging nappe and hydraulic jump (Figure 3, square). 3.2. Hydrodynamic Simulation to Quantify Exchange Paths [15] Hydrodynamic simulation of the flume experiment without a hydraulic jump represented the M2 water surface profile (i.e., convex lowering of water depth) upstream of the step, the clinging nappe down the step, and the uniform sloping water surface profile downstream of the step. Upstream of the fully penetrating step there was upwelling, and upstream of the partially penetrating step there was downwelling. Beneath the clinging nappe a shallow downwelling zone 2 cm long extended 0.5 cm into the streambed (Figure 4a) where it diverged into upstreamdirected and downstream-directed upwelling (Figure 4b). The upstream-directed upwelling component established a miniature reversed hyporheic circulation cell and flow reversal set within larger flow paths of downstreamdirected upwelling. The flow path predictions agreed with observed flow paths. The vertical and horizontal components of streambed hyporheic flux were plotted to compare magnitudes and identify directional changes (Figure 4c). The magnitude of the peak downstream-directed upwelling flux was equal to the peak downwelling flux (Figure 4c). The downstream-directed horizontal flux magnitude was greatest along the step base and immediately downstream of the nappe. The upstream-directed horizontal flux was approximately 10% of the maximum downstream flux magnitude. Upstream-directed fluxes occupied a single zone abutting the step and were less than 5% of the 13.5 cm long streambed immediately downstream of the step. Without the jump, downstream flux was constrained to a small zone beneath the nappe and had little spatial extent or depth. [16] Hydraulic jump simulations generated the rapidly varied flow and water surface profile similar to the profile

Figure 3. Sketch of flow paths observed in the flume experiment with (a) no hydraulic jump, shallow downwelling beneath the nappe, and otherwise uniform downstream-directed upwelling and (b) a hydraulic jump and zones of upstream-directed flow beneath the jump, downwelling beneath the nappe, and shallow downwelling beneath the standing wave. observed in the flume, including the presence of rollers in the jump profile. There was good agreement between the CFD and flume exchange paths upstream of the step for fully and partially penetrating steps. Upstream of the step, the drawdown in the water surface profile (i.e., flow of decreasing depth and increasing velocity) generated a 1 cm long by 1 cm deep upwelling zone along the step’s upstream edge. Downstream of the step the model predicted a downwelling zone beneath the nappe, which matched the general location of the observed downwelling (Figure 5a). There were one or two additional downwelling zones 30 cm beyond the step along the positive slope of the jump. These downwelling zones were associated with standing waves and they generally agreed with isolated downwelling observed under waves in the flume. Upstream-directed fluxes were predicted beneath the nappe, along the adverse slope of the jump, and beneath the standing waves (Figure 5b). A reversed hyporheic circulation cell was identified beneath the nappe, and a flow reversal was below this cell and below the hydraulic jump. Streambed flux direction and magnitude were plotted to quantify exchange patterns.

Figure 2. Glass-walled flume experiments with fully penetrating step (a) for the case of no hydraulic jump showing the dye injection site for the following image, (b) with downstream-directed upwelling; and (c) for the case of a hydraulic jump showing the dye injection sites for the following two images, (d) with downwelling beneath the nappe, and (e) upstreamdirected upwelling below the jump. 5 of 10

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Figure 4. Hydrodynamic model depiction of the flume experiment without the hydraulic jump; arrows showing some flow paths over (a) vertical fluxes and (b) horizontal fluxes. (c) Graph of vertical and horizontal hyporheic flux at streambed interface.

Figure 5. Hydrodynamic model depiction of the flume experiment with the hydraulic jump; arrows showing some flow paths over (a) vertical fluxes and (b) horizontal fluxes. (c) Graph of vertical and horizontal hyporheic flux at streambed interface.

The reversed hyporheic circulation cell is identified in the streambed flux plot, where the vertical downwelling flux overlaps the downstream edge of upstream-directed horizontal flux. Upwelling fluxes had peak magnitudes immediately downstream of the step and were of equal magnitude to the maximum downwelling flux beneath the impinging jet (Figure 5c). The maximum upstream-directed flux beneath the jump was only 25% of the maximum upstreamdirected flux at the impinging jet, but had more than twice the spatial extent. Upstream-directed fluxes from these two zones occupied 75% of the 13.5 cm long streambed immediately downstream of the step. Downwelling flux beneath the nappe occupied 25% of this streambed length and penetrated into 10% of the streambed volume beneath the 13.5 cm downstream length. [17] Contour plots of model-estimated hydraulic head (Figure 6a), velocity head (Figure 6b), and pressure head

(Figure 6c) were generated for the hydraulic jump scenario to identify dynamic head (i.e., velocity head dominates signal) and static head (i.e., at a stagnation point where velocity head is converted to pressure head) patterns governing hyporheic exchange. The maximum downwelling flux was spatially congruent with a local maximum hydraulic head situated below the impinging jet. At this stagnation point the velocity head becomes zero and is converted into static pressure head. The local mounding of pressure head causes the divergence of downwelling into upstream-directed and downstream-directed flux. These horizontal fluxes turn toward the local hydraulic head minima on either side of the impinging jet. A flatter and lower mounding of pressure head is located beneath the jump. The velocity head in this zone is relatively constant, but the elevation head is changing with the water surface profile and increases in the downstream direction. This

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and velocity. Without the hydraulic jump, gradually varied flow predominated below the step, except along the step face where the nappe was established. In gradually varied flow the flow depth changes with downstream distance but remains either larger or smaller than the normal depth and does not cross the critical depth. With the hydraulic jump, rapidly varied flow predominated below the step, crossing normal and critical depths. [19] There was little spatial complexity to the exchange patterns without the jump, and exchange patterns were mostly associated with the spatial change in velocity and water surface profile along the gradually varied flow. Without the hydraulic jump, downstream-directed upwelling occupied 99% of the downstream streambed volume. This dominant spatial pattern of exchange was attributed to the step followed by a uniform water surface profile sloping at 1% with the streambed. The only deviation was at the nappe, which had limited spatial extent and generated weak stagnation pressure due to high drag along the step face. Turbulence observed beneath the nappe could lead to turbulent diffusion as an exchange mechanism [Nagaoka and Ohgaki, 1990; Packman et al., 2004], transporting dye into the streambed 2 – 10 times the mean diameter of the substrate [Tonina and Buffington, 2009]. While turbulence may have contributed to exchange, the patterns of upstreamdirected upwelling are attributed to advective forces established by the velocity and pressure head.

Figure 6. Hydrodynamic model-estimated (a) hydraulic head, (b) velocity head, and (c) pressure head with the hydraulic jump. downstream mounding of pressure head causes the relatively weak upstream-directed downwelling flux. In cases with no hydraulic jump, the pressure mound below the clinging nappe was limited to a 1 cm section of streambed and the downstream pressure contour sloped uniformly with the bed.

4.

Discussion

4.1. Contrasting Rapidly and Gradually Varied Flow [18] In the flume and model step analysis, the presence of the hydraulic jump was controlled by changing discharge, so comparison of hyporheic exchange with and without a hydraulic jump also involved a change in the flow depth

4.2. Upstream-Directed Hyporheic Flux Beneath the Jump [20] Upstream-directed hyporheic flux was recorded by Elliott and Brooks [1997a] (see their Figure 2) in flume experiments with steady flow along triangular-shaped bed forms. The water surface profile for these experiments was a constant slope, and velocity along the bed was described with a sinusoidal function. Velocity was slowest and pressure highest midway along the upstream face of the bed form and velocity was fastest and pressure lowest along the downstream face between the bed form crest and trough [Elliott and Brooks, 1997a]. Flume water entered the hyporheic zone along the lower upstream face as upstreamdirected downwelling and exited at the trough as upstreamdirected upwelling. A sinusoidal head pumping model was developed and applied to a flat bed to replicate the flux paths observed in triangular bed forms [Elliott and Brooks, 1997b]. The upstream-directed flux we observed under the nappe was also initiated by coupled changes in pressure head and velocity head, but the pattern was not governed by bed form wavelength and amplitude. The pressure head and velocity head changed abruptly along the step profile. If we introduced conditions common to natural rivers, such as pulsating flow or entrainment of air into the nappe or jet, the upstream-directed upwelling might have temporal variation. Compared with the flux under the nappe, the larger zone of upstream-directed flux we observed under the jump was governed more by the water surface profile than by velocity head. The influence of the hydraulic jump on upstream-directed flux was depicted by Tonina and Buffington [2009, Figure 7a] in their graphic of a hyporheic exchange model along a riffle-pool sequence. When the jump was present at 8% of bankfull discharge a small zone of upstream-directed upwelling flux was present midway

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along the jump, and this flux disappeared with the jump when discharge was increased to bankfull conditions [Tonina and Buffington, 2009]. The dynamic forces associated with velocity head and the static forces associated with the water surface profile can establish upstream-directed flux and associated hyporheic exchange cells and flow reversals within otherwise downstream-directed hyporheic flow nets. 4.3. Downwelling Flux Beneath the Nappe [21] Downwelling beneath the nappe extended 3 cm down into the bed with a partially penetrating step and 5 cm with a full penetrating step, nearly reaching the base of our 6 cm deep bed. It is possible these downwelling zones below the nappe or standing waves could cause field piezometers below steps to record downwelling vertical hydraulic gradients (VHGs). The VHG is a measure of vertical flux potential between the streambed and top of the piezometer screen. The conceptual model of hyporheic exchange at steps is downwelling upstream of the step along the convex water surface profile and upwelling downstream of the step along the concave water surface profile [Harvey and Bencala, 1993; Tonina and Buffington, 2009]. There have been reports of piezometers situated below steps not observing the upwelling VHG predicted by conceptual and hydrostatic groundwater models [Fanelli and Lautz, 2008]. This happened in three nonlosing headwater reaches in the Cascade Mountains, where Wondzell [2006] predicted upwelling should be present on the basis of groundwater model hydraulic gradients and step-pool morphology. Similarly, Anderson et al. [2005] reported the absence of upwelling in the majority of piezometers below steps, despite the prediction of upwelling based on steppool morphology and associated water surface concavity. From our experiments the downwelling fluxes beneath the nappe were not deep enough to explain the absence of upwelling fluxes in pools beneath steps when piezometer screens are between 15 and 100 cm below the streambed. In natural rivers with a gravel substrate the downwelling depth beneath the nappe may remain shallow if they are constrained by strong regional fluxes of upwelling water. However, if the boulder steps have greater penetration depths they block regional flows and allow for greater downwelling extents. If this downwelling were situated above a more deeply buried cobble, there is further protection from regional upwelling fluxes. In natural rivers changes in step height or discharge could also increase in the stagnation pressure below the nappe. Variations in substrate heterogeneity, step geometry, and discharge could result in downwelling depths entering the range of field piezometers and explain why some researchers are observing downwelling VHGs below steps. This may be the first field application of our refined conceptual model for exchange sequences along steps with rapidly varied flow. 4.4. Spatial Variation in Hyporheic Fluxes and Ecosystem Implications [22] The increased heterogeneity in hyporheic fluxes with the hydraulic jump may potentially regulate hyporheic biogeochemistry and ecosystems. The hyporheic zone is an important stream habitat [Stanford and Ward, 1988], interacting with other stream ecosystems [Findlay, 1995].

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Our flume experiment showed a 4 cm step can generate fluctuations in downstream pressure head and reversals in vertical and horizontal flux. Such steps and associated hydraulic jumps at steps or within cascades and riffles may generate intense downwelling fluxes of aerated water. We use hyporheic nitrate concentration data from a separate study to examine the potential implications of our research results for biogeochemistry of redox-sensitive solutes. In the characterization of nitrate concentration in the hyporheic zone of a mountain stream, Lautz and Fanelli [2008] showed reduction and oxidation zones were organized around a restoration structure with a pool upstream and turbulent riffle downstream. Within the riffle section they mapped a mosaic of nitrate concentrations, and these patterns shifted between October 2005 and July 2006 [Lautz and Fanelli, 2008]. The spatial mosaic of nitrate concentrations was not explained by patterns of rapidly varied flow. However, our research suggests rapidly varied flow along the gravel and cobble in the riffle might trigger concentrated zones of downwelling or upwelling, and these might regulate nitrate concentrations. The spatial heterogeneity and scale of these fluxes may create spatially significant mosaics in hyporheic habitat and ecosystems and potentially inform river restoration. 4.5. Future Research [23] Our characterization of hyporheic flow paths and their spatial extent might change with modifications to our experiment. Experimental modifications which would likely impact our results include: (1) changing flow depth, (2) changing pool shape from flat to concave, (3) introducing a sequence of steps and varying step-pool wavelength, (4) changing step height, or (5) changing the channel substrate distribution and depth. Variation in flow depth, pool shape, and step geometry would likely change the nappe and its downwelling flux location and magnitude. Changes in these features may result in changes to the pattern of upstream-directed upwelling beneath the jump. The temporal variation in jump dynamics (e.g., pulsating waves, rollers, moving sediment) was not explored, and additional experiments with refined instrumentation might consider these dynamics on hyporheic exchange. Air entrainment in the nappe or jump [Valle´ and Pasternack, 2002] influences near-bed pressure distributions [Pasternack et al., 2007] and would create spatial and temporal variation in hyporheic exchange. With sediment transport simulations we could examine how step geometry evolves beneath a hydraulic jump [Comiti and Lenzi, 2006] and changes the pattern of hyporheic exchange.

5.

Conclusions

[24] Rapidly varied flow downstream of a step generates a water surface profile with several breaks in slope and changes in velocity. Features of the flow include drawdown upstream of the step, a nappe, an impinging jet, and a hydraulic jump, possibly with undulating waves. Downwelling beneath the nappe occupied a length of streambed equal to 3/4 of step height, and occupied 25% of the first 13.5 cm of streambed beyond the step. The depth of downwelling increased from 3 to 5 cm when the step penetrated deeper into the bed and blocked regional upwelling

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fluxes. Upstream-directed upwelling beneath the jump typically extended the length of the jump and occupied 75% of the first 13.5 cm of streambed beyond the step. The depth of upstream-directed flux increased from 3 to 6 cm below the bed when the step changed from partially to fully penetrating. [25] The previous conceptual model of hyporheic exchange at a partially penetrating step involved downstream-directed downwelling above the step connecting to downstream-directed upwelling below the step. This model accounted for water surface convexity upstream of the step and concavity downstream of the step but did not account for the velocity head changes at the nappe or the water surface profile of the jump. We used nonmobile bed flume experiments and hydrodynamic simulation to characterize flow paths around the hydraulic jump below a step. Our refined conceptual model of hyporheic exchange at a partially penetrating step involves the same downstreamdirected downwelling above the step with the addition of the following: (1) a narrow but high magnitude upwelling flux along the downstream face of the step, (2) a downwelling flux beneath the impinging jet of the nappe which diverges into equal parts upstream-directed and downstream-directed upwelling, (3) upstream-directed upwelling flux beneath the length of the jump, and (4) additional downwelling fluxes beneath waves in the jump. These flux paths are nested within a larger flow net of downstreamdirected upwelling. We define the transition between upstream-directed downwelling and upstream-directed upwelling fluxes as a reversed hyporheic circulation cell, and the transition of downstream-directed upwelling to upstream-directed-upwelling as a flow reversal. [26] Acknowledgments. This research was funded by the National Science Foundation under grants 0450317 and 0836354. Editorial assistance from E. Wohl and comments from E. Hester and two anonymous reviewers were extremely useful in manuscript revisions. Flume steps were engineered by B. Reschke.

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T. Endreny, Environmental Resources Engineering, 423 Baker Labs, SUNY School of Environmental Science and Forestry, Syracuse, NY 13210, USA. ([email protected]) L. Lautz and D. I. Siegel, Earth Sciences, 204 Heroy Geology Labs, Syracuse University, Syracuse, NY 13210, USA. ([email protected]; [email protected])

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