Strain-vorticity induced secondary motion in shallow flows

Space discontinuous Galerkin method for shallow water flows —kinetic and HLLC flux, and potential vorticity generation

In this paper, a second order space discontinuous Galerkin (DG) method is presented for the numerical solution of inviscid shallow water flows over varying bottom topography. Novel in the implementation is the use of HLLC and kinetic numerical fluxes 1 in combination with a dissipation operator, applied only locally around discontinuities to limit spurious numerical oscillations. Numerical solu...

Local and nonlocal strain rate fields and vorticity alignment in turbulent flows.

Local and nonlocal contributions to the total strain rate tensor S(ij) at any point x in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor S(ij)(B)(x) to be obtained from S(ij)(x). In turbulent flows, where the vorticity naturally concentra...

Shallow Water Flows in Channels

We consider the shallow water equations for flows through channels with arbitrary cross-section. The system forms a hyperbolic set of balance laws. Exact steady-state solutions are available and are controlled by the relation between the bottom topography and the channel geometry. We use a Roetype upwind scheme for the system. Considerations of conservation, near steady-state accuracy, velocity...

Nonclassical Shallow Water Flows

This paper deals with violent discontinuities in shallow water flows with large Froude number F . On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity ...

Shallow granular flows