Azimuthal equatorial flows in spherical coordinates with discontinuous stratification

Abstract

We are concerned here with an exact solution to the governing equations for geophysical fluid dynamics in spherical coordinates which incorporates discontinuous fluid stratification. This solution represents a steady, purely--azimuthal equatorial flow with an associated free-surface and an interface separating two fluid regions, each of which having its own continuous distribution of density. However, the two density functions do not match along the interface. Following the derivation of the solution we demonstrate that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface's shape. Moreover, imposing the continuity of the pressure along the interface generates an equation that describes (implicitly) the shape of the interface. Interestingly, it turns out that the interface defining function has infinite regularity.

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References in corpus (6)

• Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates
• Hamiltonian model for coupled surface and internal waves in the presence of currents
• Effects of vorticity on the travelling waves of some shallow water two-component systems
• On the intermediate long wave propagation for internal waves in the presence of currents
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Cited by in corpus (2)

• Liouville-type results for time-dependent stratified water flows over variable bottom in the $\beta$-plane approximation
• Three-layer water flows: Dirichlet-Neumann operators and approximations