TL;DR: In this paper, a metadata analysis of 563 direct gas tracer release experiments was conducted to examine scaling laws for the gas transfer velocity and the product of stream slope and velocity, which is in alignment with theory on stream energy dissipation.
Abstract: Scaling is an integral component of ecology and earth science. To date, the ability to determine the importance of air – water gas exchange across large spatial scales is hampered partly by our ability to scale the gas transfer velocity and stream hydraulics. Here we report on a metadata analysis of 563 direct gas tracer release experiments that examines scaling laws for the gas transfer velocity. We found that the gas transfer velocity scales with the product of stream slope and velocity, which is in alignment with theory on stream energy dissipation. In addition to providing equations that predict the gas transfer velocity based on stream hydraulics, we used our hydraulic data set to report a new set of hydraulic exponents and coefficients that allow the prediction of stream width, depth, and velocity based on discharge. Finally, we report a new table of gas Schmidt number dependencies to allow researchers to estimate a gas transfer velocity using our equation for many gasses of interest.
TL;DR: In this article, the authors used two-dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second-, third-, and fourth-order mountain stream reaches.
Abstract: Studies of hyporheic exchange flows have identified physical features of channels that control exchange flow at the channel unit scale, namely slope breaks in the longitudinal profile of streams that generate subsurface head distributions. We recently completed a field study that suggested channel unit spacing in stream longitudinal profiles can be used to predict the spacing between zones of upwelling (flux of hyporheic water into the stream) and downwelling (flux of stream water into the hyporheic zone) in the beds of mountain streams. Here, we use two-dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second-, third-, and fourth-order mountain stream reaches. Modelling allowed us to (1) represent visually the effect that the shape of the longitudinal profile has on the flow net beneath streambeds; (2) isolate channel unit sequence and spacing as individual factors controlling the depth that stream water penetrates the hyporheic zone and the length of upwelling and downwelling zones; (3) evaluate the degree to which the effects of regular patterns in bedform size and sequence are masked by irregularities in real streams. We simulated hyporheic exchange in two sets of idealized stream reaches and one set of observed stream reaches. Idealized profiles were constructed using regression equations relating channel form to basin area. The size and length of channel units (step size, pool length, etc.) increased with increasing stream order. Simulations of hyporheic exchange flows in these reaches suggested that upwelling lengths increased (from 2Ð 7mt o 7 Ð6 m), and downwelling lengths increased (from 2Ð 9mt o 6 Ð0 m) with increase in stream order from second to fourth order. Step spacing in the idealized reaches increased from 5Ð 3mt o 13Ð7 m as stream size increased from second to fourth order. Simulated downwelling lengths increased from 4Ð 3m in second-order streams to 9Ð7 m in fourth-order streams with a POOL–RIFFLE–STEP channel unit sequence, and increased from 2Ð 5m to 6 Ð1 m from second- to fourth-order streams with a POOL–STEP–RIFFLE channel unit sequence. Upwelling lengths also increased with stream order in these idealized channels. Our results suggest that channel unit spacing, size, and sequence are all important in determining hyporheic exchange patterns of upwelling and downwelling. Though irregularities in the size and spacing of bedforms caused flow nets to be much more complex in surveyed stream reaches than in idealized stream reaches, similar trends emerged relating the average geomorphic wavelength to the average hyporheic wavelength in both surveyed and idealized reaches. This article replaces a previously published version (Hydrological Processes, 19(17), 2915–2929 (2005) [DOI:10.1002/hyp.5790]. Copyright 2006 John Wiley & Sons, Ltd.
TL;DR: In this article, a model was developed to predict the advective flow induced in a sand bed by stream flow over bedforms, and the resulting "pumping" exchange rate was calculated based on the streamflow conditions, bed form geometry, and bed depth.
Abstract: Fine sediment exchange between a stream and the surrounding subsurface influences downstream contaminant transport and stream ecology. Fundamental models for this exchange were developed on the basis of (1) the hydraulics of bed form-driven advective pore water flow and (2) subsurface colloid transport processes. First, a model was developed to predict the advective flow induced in a sand bed by stream flow over bedforms. The resulting “pumping” exchange rate was calculated based on the streamflow conditions, bed form geometry, and bed depth. The pumping exchange of suspended sediment was then calculated by superimposing advective transport and particle settling in the bed and including the effect of physicochemical filtration by bed sediment. The filtration coefficient approach was used to predict the reduction in the concentration of transported particles. Both settling and filtration cause colloids to be trapped in stream beds, producing a higher net exchange rate relative to conservative solutes. When transported particles are completely trapped in a single pass through the bed, the exchange calculation is simplified because only the particle flux to the bed must be considered. In this case, the net exchange rate may be adequately represented by an effective piston velocity (flux/concentration) or loss rate to the bed in the advection-dispersion equation for the stream. Solute and colloid exchanges are predicted by the models without the use of fitting coefficients; only measurable hydraulic and particle parameters were used as model inputs. Simulations are presented which show the effect of stream parameters, settling, and filtration on net particle exchange. This fundamental approach to modeling stream-subsurface exchange potentially has great utility for understanding and predicting the transport and fate of reactive substances in streams.
TL;DR: In this article, the slope-dependent variation in critical mean bed shear stress for coarse grain motion was investigated, and the effect of slope on both critical stream power per unit bed area and critical MEB stress was investigated.
TL;DR: In this article, a rational expression relating stream variables and fluid properties which define the reaeration rate constant, k2, was found to be directly proportional to average stream Telocity and inversely proportional to the average stream depth raised to the 3/2 power.
Abstract: A simulated stream channel was used in laboratory investigations to determine a rational expression relating stream variables and fluid properties which define the reaeration rate constant, k2. Direct measurement of the reaeration coefficient at controlled depths and stream velocities enabled the development of a dimensionally homogeneous expression for k2. The developed expression accounts for variations in k2 due to changes in temperature as well as changes in fluid flow conditions. For the rectangular cross section employed in these studies, the reaeration rate constant, k2, was found to be directly proportional to average stream Telocity, and inversely proportional to the average stream depth raised to the 3/2 power. The constant of proportionality was found to be 3.053. When the same analytical approach was applied to the best available natural stream data, the proportionality constant obtained was 3.739. Both analyses yielded highly acceptable correlation coefficients. It is believed that the difference in the values of the proportionality constant is due primarily to differences in channel geometry, i.e., smooth rectangular laboratory channel versus irregular-shaped natural river channels.