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Free surface equatorial flows in spherical coordinates with discontinuous stratification depending on depth and
Calin Martin1, Adrian Petruşel2,3
1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
Annali Di Matematica Pura Ed Applicata
|October 24, 2022
Summary
This study presents an exact geophysical fluid dynamics solution for equatorial flows, detailing a two-layer system with a discontinuous density interface. The research clarifies the relationship between free-surface pressure and shape, and the interface
Area of Science:
- Geophysical Fluid Dynamics
- Fluid Mechanics
- Oceanography
Background:
- Equatorial flows are crucial in Earth's climate system.
- Understanding discontinuous stratification is key to modeling ocean and atmospheric dynamics.
- Exact solutions provide fundamental insights into complex fluid behaviors.
Purpose of the Study:
- To derive and analyze an exact solution for geophysical fluid dynamics equations.
- To describe steady, purely-azimuthal equatorial two-layer flow.
- To investigate discontinuous fluid stratification varying with depth and latitude.
Main Methods:
- Derivation of exact solutions in spherical coordinates.
- Analysis of steady, purely-azimuthal two-layer flow.
- Implicit representation of free-surface and interface shapes.
Main Results:
- An exact solution for equatorial flows with discontinuous stratification was obtained.
- Explicit formulas for velocity and pressure were derived.
- A relationship between free-surface pressure and shape was established, and the interface shape was implicitly defined.
Conclusions:
- The derived solution offers a fundamental model for equatorial two-layer flows.
- The study provides insights into the dynamics of discontinuous density interfaces.
- A regularity result for the interface was established under specific assumptions.
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