Casimir-dissipation stabilized stochastic rotating shallow water equations on the sphere. (English) Zbl 07789304
Nielsen, Frank (ed.) et al., Geometric science of information. 6th international conference, GSI 2023, St. Malo, France, August 30 – September 1, 2023. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 14072, 253-262 (2023).
Summary: 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.
For the entire collection see [Zbl 1528.53002].
For the entire collection see [Zbl 1528.53002].
MSC:
76M35 | Stochastic analysis applied to problems in fluid mechanics |
76U05 | General theory of rotating fluids |
76E07 | Rotation in hydrodynamic stability |
Keywords:
structure preserving discretization; potential enstrophy; Laplacian diffusion; barotropically unstable jet flowReferences:
[1] | Bauer, W.; Gay-Balmaz, F., Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations, J. Comput. Dyn., 6, 1, 1-37 (2019) · Zbl 1421.76189 |
[2] | Brecht, R.; Bauer, W.; Bihlo, A.; Gay-Balmaz, F.; MacLachlan, S., Selective decay for the rotating shallow-water equations with a structure-preserving discretization, Phys. Fluids, 33 (2021) · doi:10.1063/5.0062573 |
[3] | Brecht, R., Li, L., Bauer, W., Mémin, E.: Rotating shallow water flow under location uncertainty with a structure-preserving discretization. J. Adv. Model. Earth Syst. 13, e2021MS002492 (2021) |
[4] | Galewsky, J.; Scott, RK; Polvani, LM, An initial-value problem for testing numerical models of the global shallow-water equations, Tellus A: Dyn. Meteorol. Oceanogr., 56, 5, 429-440 (2004) · doi:10.3402/tellusa.v56i5.14436 |
[5] | Gay-Balmaz, F.; Holm, D., Selective decay by Casimir dissipation in inviscid fluids, Nonlinearity, 26, 2, 495 (2013) · Zbl 1322.76036 · doi:10.1088/0951-7715/26/2/495 |
[6] | Mémin, E., Fluid flow dynamics under location uncertainty, Geophys. Astrophys. Fluid Dy., 108, 2, 119-146 (2014) · Zbl 1541.76026 · doi:10.1080/03091929.2013.836190 |
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