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We introduce a structure preserving discretization of stochastic rotatingshallow water equations, stabilized with an energy conserving Casimir (i.e.potential enstrophy) dissipation. A stabilization of a stochastic scheme isusually required as, by modeling subgrid effects via stochastic processes,small scale features are injected which often lead to noise on the grid scaleand numerical instability. Such noise is usually dissipated with a standarddiffusion via a Laplacian which necessarily also dissipates energy. In thiscontribution we study the effects of using an energy preserving selectiveCasimir dissipation method compared to diffusion via a Laplacian. For both, weanalyze stability and accuracy of the stochastic scheme. The results for a testcase of a barotropically unstable jet show that Casimir dissipation allows forstable simulations that preserve energy and exhibit more dynamics thancomparable runs that use a Laplacian.

Casimir-dissipation stabilized stochastic rotating shallow water equations on the sphere