Singular Limits of the Shallow Water Equations on the Sphere
arXiv:2607.14257
The paper studies how solutions of the slightly compressible shallow water equations on a rapidly rotating sphere behave when the Froude and Rossby numbers become small, proving uniform bounds and convergence to limit equations for well‑prepared initial data.
Abstract
Solutions of the slightly compressible shallow water equations on a rapidly rotating sphere are shown to be bounded uniformly when ratio of the Froude number to the Rossby number is bounded. Moreover, in the singular limit in which the ratio of those parameters remains fixed while they both tend to zero, solutions with well-prepared initial data tend to corresponding solutions of limit equations. A convergence result is also obtained for the three-scale singular limit in which the Froude number tends to zero faster than the Rossby number.