Abstract
We introduce a structure preserving discretization of stochastic rotating
shallow water equations, stabilized with an energy conserving Casimir (i.e.
potential enstrophy) dissipation. A stabilization of a stochastic scheme is
usually required as, by modeling subgrid effects via stochastic processes,
small scale features are injected which often lead to noise on the grid scale
and numerical instability. Such noise is usually dissipated with a standard
diffusion via a Laplacian which necessarily also dissipates energy. In this
contribution we study the effects of using an energy preserving selective
Casimir dissipation method compared to diffusion via a Laplacian. For both, we
analyze stability and accuracy of the stochastic scheme. The results for a test
case of a barotropically unstable jet show that Casimir dissipation allows for
stable simulations that preserve energy and exhibit more dynamics than
comparable runs that use a Laplacian.