Transcritical shallow-water flow past topography: finite-amplitude theory

Transcritical shallow-water flow past topography: finite-amplitude theory

We consider shallow-water flow past a broad bottom ridge, localized in the flow direction, using the framework of the forced Su–Gardner (SG) system of equations, with a primary focus on the transcritical regime when the Froude number of the oncoming flow is close to unity. These equations are an asymptotic long-wave approximation of the full Euler system, obtained without a simultaneous expansi...

Critical controls in transcritical shallow-water flow over obstacles

The nonlinear shallow-water equations are often used to model flow over topography In this paper we use these equations both analytically and numerically to study flow over two widely separated localised obstacles, and compare the outcome with the corresponding flow over a single localised obstacle. Initially we assume uniform flow with constant water depth, which is then perturbed by the obsta...

Generation of internal undular bores by transcritical flow over topography

In both the ocean and the atmosphere, the interaction of a density stratified flow with topography can generate large-amplitude, horizontally propagating internal solitary waves. Often these waves appear as a wave-train, or undular bore. In this article we focus on the situation when the flow is critical, that is, the flow speed is close to that of a linear long wave mode. In the weakly nonline...

Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions

The initial data and bottom topography, used as inputs in shallow water models, are prone to uncertainty due to measurement errors. We model this uncertainty statistically in terms of random shallow water equations. We extend the Multi-Level Monte Carlo (MLMC) algorithm to numerically approximate the random shallow water equations efficiently. The MLMC algorithm is suitably modified to deal wit...

Investigating vortex dynamics in shallow water with topography