A shallow-water model for hydraulically transcritical flows

Abstract

This document describes a numerical model that was developed to study two-dimensional, reduced-gravity, shallow-water flows. When the dynamics of these flows is strongly nonlinear, the flow may become hydraulically supercritical and discontinuities in the flow field may arise. The presence of discontinuities in the flow field requires a special numerical treatment in order to maintain both accuracy and stability in the numerically-approximated solution. In this model, a shock-capturing scheme called the Essentially Non-Oscillatory (ENO) scheme is implemented. The ENO scheme is a high-order, adaptive-stencil, finite-difference, characteristic-based scheme for hyperbolic equations that has been applied widely to flows governed by the Euler equations of gas dynamics. The model described in this document was developed for geophysical applications, and therefore includes the effects of rotation (constant Coriolis parameter), forcing (time dependent and/or spatially varying), and bottom drag (linear or nonlinear). The presentation includes the mathematical formulation of the model as well as instructions on how to prepare and execute model runs.