Numerical modelling of flow, transport and reactions in hyporheic zones

Author: Tariq Laattoe

Laattoe, Tariq, 2016 Numerical modelling of flow, transport and reactions in hyporheic zones, Flinders University, School of the Environment

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Hyporheic exchange is perhaps the quintessential ground and surface water interaction. It involves a continuous cycle of exchange between surface waters in streams or rivers and the pore water in their bed or bank sediments. It is now recognized as one of the most important zones in a riverine ecosystem that controls the dynamics of surface water quality. Prior to the work of Thibodeaux and Boyle (1987) the process was considered to be governed by diffusion, but their tracer experiment in a flume replicating a stream with a waveform structure on the streambed, identified advective currents in the bed sediments. Detail of the pressure distribution created by water flowing over the streambed in that experiment was soon used to develop a two dimensional numerical model, leading to the first hyporheic zone bedform model. Current research in the hyporheic zone covers significantly larger spatial and temporal scales. However, the bedform (< 1.0 m) scale remains a popular area for investigating hyporheic zone (HZ) process dynamics.

One of the most popular bedform scale numerical models features a boundary condition used to approximate an infinite repetition of space. Known as a spatially periodic boundary (SPB), it is a feature common to numerous computational fluid dynamics software packages but lacking in the industry standard groundwater modelling software MODFLOW. Indeed, MODFLOW, its related solute transport code MT3DMS, and reactive transport variant PHT3D, are all generally underutilized in the area of bedform scale HZ research. Use of the single bedform model has expanded to include solute, thermal and reactive transport variants featured in multiple studies where spatial periodicity with respect to transport is also enforced.

This body of work attempts to further examine HZ processes at the bedform scale adopting the combined spatially periodic flow and transport boundary condition and concurrently promote the use of MODFLOW, MT3DMS and PHT3D in future HZ studies through development of the spatially periodic boundary condition. Specifically this work achieves the following: 1) develops, implements and assess the function of a spatially periodic boundary condition in MODFLOW; 2) Examines the effects of the periodic assumption with conservative solute transport variants of the single-bedform model; 3) develops, implements and assess the function of a spatially periodic boundary condition in MT3DMS; and 4) examines the effect of the periodic assumption on reactive transport simulations common to the single bedform model using PHT3D.

The first part of this study presents a method to implement the SPB in MODFLOW through development of the appropriate block-centered finite difference expressions. A source code modification is then made to MODFLOW’s general head boundary package. The modifications are verified through a comparison of modelled results with an analytical solution of a sinusoidal head distribution over a flat streambed across a horizontally infinite domain. A second verification is also presented using a series of multi-bedform models with increasing bedform numbers to determine if the central bedform in each multi-bedform model converges on the single bedform solution.

The second part of this study uses the spatially periodic flow boundary to develop a multi-bedform model with a steady-state spatially-periodic flow field. Solute distributions at an approximate steady state are then obtained for the flow field using MT3DMS and used to demonstrate a physically realistic transport solution with a spatially periodic flow filed. The results indicate that lack of symmetry between the boundaries is a function of the vertical concentration gradient and two dimensionless parameters, which characterize the hyporheic and underflow regimes, and the solute exchange between them. A thermal scenario with sinusoidal temperature variation at the surface is also examined and demonstrates that the reversal of the thermal gradient across the streambed surface promotes a spatially periodic solution. The study concludes that the solute variant of the spatially periodic boundary condition should be applied only to single-bedform models with minimal vertical diffusive and dispersive solute transfer.

The third part of this study develops the solute variant of the spatially periodic boundary for MT3DMS and PHT3D. The appropriate block-centered finite-difference approach to implementing the boundary is presented along with the necessary source code modifications to MT3DMS’s sink source mixing package. The performance of the boundary is explored through comparison of a multi-bedform hyporheic zone model with a single bedform model. The boundary condition demonstrates appropriate performance for situations where dispersive effects and lateral seepage flux are minimal.

The fourth part of this study examines the effects of the solute SPB in PHT3D on a reactive transport variant of the single bedform model. Comparisons are made with a similar multi-bedform model. The reactive transport comprises a modified Monod kinetics model of dissolved organic carbon degradation, nitrification and denitrification. The solutions produced by the single bedform model are compared to the downstream trends observed in the multi-bedform model. A Damköhler number for each reactant species is used as a metric for reactivity comparison between bedforms. The results demonstrate that the solute SPB can produce single bedform solutions indicative of a nitrate sink while the corresponding multi-bedform model solution is that of a nitrate source. Observations also indicate that mixing, currently neglected in many HZ studies, has implications for studies linking reaction rates specifically to HZ residence time.

Keywords: hyporheic, bedform, numerical model, reactive transport, solute transport, spatially periodic boundary

Subject: Environmental Science thesis

Thesis type: Doctor of Philosophy
Completed: 2016
School: School of the Environment
Supervisor: Dr. Vincent Post