Effects of the Turbulent Schmidt Number on the Mass Exchange of a Vegetated Lateral Cavity

<p>Computational Fluid Dynamics (CFD) has been established as a relevant technique to investigate the qualitative and quantitative characteristics of complex environmental flows, such as transient storage zones. In numerical studies involving mass transport of solutes and sediment (e.g., mean retention time and mass exchange rate), one fundamental variable is the turbulent Schmidt number (Sct) which defines the ratio of momentum diffusivity to mass diffusivity in turbulent flows, and thus affects the concentration of solute within the solution impacting on the estimation of mass related variables. This is particularly important for transient storage zones, such as lateral cavities and groyne fields, as they are known for their role in nutrient retention and release, and sediment entrapment. This numerical study aims to examine the influence of the turbulent Schmidt number in the mean retention time and mass exchange rate between a channel and a vegetated/non-vegetated lateral cavity.</p><p> </p><p>The cavity was <em>L</em> = 0.25m long (x-axis), <em>W</em> = 0.15m wide (y-axis) and had a depth of <em>H</em> = 0.10m (z-axis). The aspect ratio between the width and the length resulted in 0.6 which corresponded to a single circulation system (Sukhodolov et al., 2002). The flow had a bulk velocity of <em>U</em> = 0.101 m/s that corresponds to a Reynolds number of 9000. The vegetation drag was represented by an anisotropic porous media calculated with the Darcy-Forchheimer model (Yamasaki et al., 2019), the vegetation density was constant at <em>a</em> = 0.1332%. Large Eddy Simulation (LES) was applied to define the flow field in that domain, using the Wall Adapting Local Eddy-viscosity (WALE) to account subgrid effects. A passive scalar was injected inside the lateral cavity to investigate its transport and diffusion in a range of Sct from 0.1 to 2.0. The numerical results of the flow field were validated using literature experimental data considering 3 different meshes to achieve mesh independence (Xiang et al., 2019).</p><p> </p><p>The effect of Sct variation was, then, analysed in both vegetated and non-vegetated scenarios, for a total of 40 different simulations. The volumetric average scalar concentration in the cavity was fitted into a first-order decay model <em>(C</em> = <em>C<sub>0</sub>.e<sup>-t/T<sub>D</sub></sup></em>), where <em>C<sub>0</sub> = 1</em> is the initial concentration, <em>t</em>  (s) is time and <em>T<sub>D</sub></em>  is the mean residence time. The mass exchange rate was defined as <em>k</em> = <em>W/(T<sub>D</sub>.U)</em> . Preliminary results showed in the vegetated scenarios a limited effect of Sct on the mass exchange rate, which varied from 1% if the Sct value was doubled.</p><p><strong>References</strong></p><p>Sukhodolov, A., Uijttewaal, W. S. J. and Engelhardt, C.: On the correspondence between morphological and hydrodynamical patterns of groyne fields, Earth Surf. Process. Landforms, 27(3), 289–305, doi:10.1002/esp.319, 2002.</p><p>Xiang, K., Yang, Z., Huai, W. and Ding, R.: Large eddy simulation of turbulent flow structure in a rectangular embayment zone with different population densities of vegetation, Environ. Sci. Pollut. Res., 26(14), 14583–14597, doi:10.1007/s11356-019-04709-x, 2019.</p><p>Yamasaki, T. N., de Lima, P. H. S., Silva, D. F., Preza, C. G. de A., Janzen, J. G. and Nepf, H. M.: From patch to channel scale: The evolution of emergent vegetation in a channel, Adv. Water Resour., doi:10.1016/j.advwatres.2019.05.009, 2019.</p>

On the Representation of Hyporheic Exchange in Models for Reactive Transport in Stream and River Corridors

Efforts to include more detailed representations of biogeochemical processes in basin-scale water quality simulation tools face the challenge of how to tractably represent mass exchange between the flowing channels of streams and rivers and biogeochemical hotspots in the hyporheic zones. Multiscale models that use relatively coarse representations of the channel network with subgrid models for mass exchange and reactions in the hyporheic zone have started to emerge to address that challenge. Two such multiscale models are considered here, one based on a stochastic Lagrangian travel time representation of advective pumping and one on multirate diffusive exchange. The two models are formally equivalent to well-established integrodifferential representations for transport of non-reacting tracers in steady stream flow, which have been very successful in reproducing stream tracer tests. Despite that equivalence, the two models are based on very different model structures and produce significantly different results in reactive transport. In a simple denitrification example, denitrification is two to three times greater for the advection-based model because the multirate diffusive model has direct connections between the stream channel and transient storage zones and an assumption of mixing in the transient storage zones that prevent oxygen levels from dropping to the point where denitrification can progress uninhibited. By contrast, the advection-based model produces distinct redox zonation, allowing for denitrification to proceed uninhibited on part of the hyporheic flowpaths. These results demonstrate that conservative tracer tests alone are inadequate for constraining representation of mass transfer in models for reactive transport in streams and rivers.

Application of Asymmetrical Statistical Distributions for 1D Simulation of Solute Transport in Streams

Analytical solutions of the one-dimensional (1D) advection–dispersion equations, describing the substance transport in streams, are often used because of their simplicity and computational speed. Practical computations, however, clearly show the limits and the inaccuracies of this approach. These are especially visible in cases where the streams deform concentration distribution of the transported substance due to hydraulic and morphological conditions, e.g., by transient storage zones (dead zones), vegetation, and irregularities in the stream hydromorphology. In this paper, a new approach to the simulation of 1D substance transport is presented, adapted, and tested on tracer experiments available in the published research, and carried out in three small streams in Slovakia with dead zones. Evaluation of the proposed methods, based on different probability distributions, confirmed that they approximate the measured concentrations significantly better than those based upon the commonly used Gaussian distribution. Finally, an example of the application of the proposed methods to an iterative (inverse) task is presented.

A comprehensive one-dimensional numerical model for solute transport in rivers

One of the mechanisms that greatly affect the pollutant transport in rivers, especially in mountain streams, is the effect of transient storage zones. The main effect of these zones is to retain pollutants temporarily and then release them gradually. Transient storage zones indirectly influence all phenomena related to mass transport in rivers. This paper presents the TOASTS (third-order accuracy simulation of transient storage) model to simulate 1-D pollutant transport in rivers with irregular cross-sections under unsteady flow and transient storage zones. The proposed model was verified versus some analytical solutions and a 2-D hydrodynamic model. In addition, in order to demonstrate the model applicability, two hypothetical examples were designed and four sets of well-established frequently cited tracer study data were used. These cases cover different processes governing transport, cross-section types and flow regimes. The results of the TOASTS model, in comparison with two common contaminant transport models, shows better accuracy and numerical stability.

A comprehensive one-dimensional numerical model for solute transport in rivers

Interactions between physical and chemical mechanisms involved in pollutant transport in rivers occur with varying degrees, depending on flow discharge and physical conditions. One of the issues that greatly affect the transport, especially in small mountain streams, is transient storage zones. The main effects include temporary retention of pollutants and reduce its concentration at the downstream and indirect impact on sorption process in the streambed. This paper proposes a one-dimensional model to simulate the pollutant transport in rivers with irregular cross-sections under unsteady flow with transient storage zones. The proposed model verified with analytical solution and comparison with 2-D model. The model application shown by two hypothetical examples and four set of real data that covers different processes governing on transport, cross-section types and flow regimes. Comparing results of the model with two common contaminant transport models show good accuracy and numerical stability of the model than other ones.