Articles | Volume 11, issue 2
Model description paper
06 Feb 2018
Model description paper |  | 06 Feb 2018

An axisymmetric non-hydrostatic model for double-diffusive water systems

Koen Hilgersom, Marcel Zijlema, and Nick van de Giesen

Abstract. The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier–Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

Short summary
This study models the local inflow of groundwater at the bottom of a stream with large density gradients between the groundwater and surface water. Modelling salt and heat transport in a water body is very challenging, as it requires large computation times. Due to the circular local groundwater inflow and a negligible stream discharge, we assume axisymmetry around the inflow, which is easily implemented in an existing model, largely reduces the computation times, and still performs accurately.