Exact, Free-Surface Equatorial Flows with General Stratification in Spherical Coordinates

Autor(en)

David Henry, Calin Iulian Martin

Abstrakt

This paper is concerned with the construction of a new exact solution to the geophysical fluid dynamics governing equations for inviscid and incompressible fluid in the equatorial region. This solution represents a steady purely-azimuthal flow with a free-surface. The novel aspect of the solution we derive is that the flow it prescribes accommodates a general fluid stratification: the density may vary both with depth, and with latitude. The solution is presented in the terms of spherical coordinates, hence at no stage do we invoke approximations by way of simplifying the geometry in the governing equations. Following the construction of our explicit solution, we employ functional analytic considerations to prove that the pressure at the free-surface defines implicitly the shape of the free-surface distortion in a unique way, exhibiting also the expected monotonicity properties. Finally, using a short-wavelength stability analysis we prove that certain flows defined by our exact solution are stable for a specific choice of the density distribution.

Organisation(en)

Externe Organisation(en)

University College Cork

Journal

Archive for Rational Mechanics and Analysis

Band

233

Seiten

497-512

Anzahl der Seiten

16

ISSN

0003-9527

DOI

https://doi.org/10.1007/s00205-019-01362-z

Publikationsdatum

07-2019

Peer-reviewed

Ja

ÖFOS 2012

101002 Analysis, 101027 Dynamische Systeme

Schlagwörter

ASJC Scopus Sachgebiete

Mechanical Engineering, Analysis, Mathematics (miscellaneous)

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/427b1d61-ff56-435f-b945-f347afb94d8c