Spatial periodicity in bed form‐scale solute and thermal transport models of the hyporheic zone

Abstract

AbstractSpatially periodic solute boundaries force symmetry across a model domain by ensuring that concentrations and concentration gradients are identical at the same location on opposite boundaries. They have been used in multiple publications on a hyporheic zone model of a single ripple or dune style bed form, including variable density flow and reactive transport variants. We evaluate simulations of multibed form models without imposing spatially periodic transport to demonstrate that nonphysical solute distributions arise from the periodic solute transport assumption. That is, the flow field within the single bed form model leads to a transport scenario that violates the forced symmetry of periodic solute boundary conditions, culminating in a physically unrealistic solute distribution. Our results show that lack of symmetry between boundaries is a function of the vertical concentration gradient and two‐dimensionless parameters characterizing the hyporheic and underflow flow regimes, and the solute exchange between them. We assess the error associated with the spatially periodic assumption based on an analysis of solute fluxes across the lateral bed form model boundaries. While the focus is on steady state concentration distributions, the implications for transient solute transport models are also discussed. We conclude that periodic solute transport boundary conditions should be applied only to bed form models that have minimal vertical dispersive and diffusive solute transfer. This includes gaining systems and tracers such as temperature, for which a temporally periodic flux reversal occurs across the top boundary.