Shallow water equations on a fast rotating surface

Bin Cheng; Steve Schochet

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arXiv · 1907.07028

Shallow water equations on a fast rotating surface

Bin Cheng·Steve Schochet

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Abstract

We prove that for rotating shallow water equations on a surface of revolution with variable Coriolis parameter and vanishing Rossby and Froude numbers, the classical solution satisfies uniform estimates on a fixed time interval with no dependence on the small parameters. Upon a transformation using the solution operator associated with the large operator, the solution converges strongly to a limit for which the governing equation is given. We also characterize the kernel of the large operator and define a projection onto that kernel. With these tools, we are able to show that the time-averages of the solution are close to longitude-independent zonal flows and height field.

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Bin Cheng, Steve Schochet. 2019-07-19. Shallow water equations on a fast rotating surface. https://arxiv.org/abs/1907.07028

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