Oral Presentation NCGRT/IAH Australasian Groundwater Conference 2019

Modelling groundwater-surface water interactions with the Double-Averaged Navier Stokes Equations: a step towards next-generation tools for integrated limit setting (275)

Andrew L. Dark 1 , John C. Bright 1
  1. Aqualinc Research Ltd., Christchurch, New Zealand


Existing coupled models for groundwater and surface water flows use different governing equations for the different components, making them reliant on numerical coupling methods that can be the source of instability and mass-balance errors.  This is currently a barrier to their use in integrated limit-setting processes.

This project investigated the feasibility of resolving these issues by using a single system of equations for both surface and subsurface flows.

Design and Methodology

A 2D numerical model (a vertical slice) was developed to solve the Double-Averaged Navier Stokes (DANS) Equations (Nikora et al., 2007), using a finite-volume implementation.  This allows the horizontal and vertical velocity components to be modelled over the depth of a stream and the underlying hyporheic zone or aquifer.

The most significant challenge in the development of the DANS numerical model was the implementation of a turbulence model that allows a transition between a turbulent free-surface flow and laminar Darcian flow in the underlying porous medium.  The model determines whether flows in the near-bed region are in a turbulent, non-linear laminar or Darcian regime, rather than specifying this a priori.


Considering "book-end" scenarios  (i.e. groundwater only; surface water only), the numerical model successfully reproduced analytical solutions and published experimental results.  For the full groundwater - surface water case, velocity and turbulent kinetic energy fields from the numerical model were compared to data from innovative particle-tracking experiments in a laboratory flume, using transparent beads as the porous medium.  The following figures show velocity fields from the lab experiments (above) and the numerical model (below) for a "gaining stream" configuration.5d02fe2026fe8-gaining1avg_UV_crop.jpg


Features of the flows measured in the laboratory were well replicated by the numerical model.


This project confirmed the technical feasibility of using the DANS Equations for modelling groundwater and surface water flows as one system.  Proposed further research will extend the model to 3D and improve the representation of processes such as the free surface, creating a model that can be used at a practical scale.  Analogies between the turbulence transport equation used in the model and the governing equations for contaminant transport suggest that the model could be extended to model contaminant transport.  The ability to model groundwater and surface water flows and transport in a single consistent mathematical framework would be a substantial step forward in reducing the cost and complexity of quantifying interdependencies between water allocation and nutrient discharge limits.


  1. Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. and Walters, R. (2007), Double-averaging concept for rough-bed open-channel and overland flows: Theoretical background. Journal of Hydraulic Engineering - ASCE, 133(8), 873-883.