Exact geophysical waves in stratified fluids

Abstract

When studying water waves travelling over an inviscid fluid at the Earth's surface there are additional Coriolis and centrifugal forces which influence the motion of the fluid particles. In particular, for waves propagating near the Equator the geophysical wave problem can be modelled by the so-called f-plane approximation. In this paper, we provide an explicit exact solution to the edge wave problem for stratified geophysical flows in the equatorial f-plane approximation.

Global diffeomorphism of the Lagrangian flow-map defining equatorially trapped water waves

“…In so doing we show that the fluid domain as a whole evolves in a manner which is consistent with the full governing equations. We note that subsequent to the derivation of Constantin's solution, a wide range of geophysical generalizations and variations to [5] have been produced and analysed, for example [6,7,8,14,16,17,18,19,20,21]. It is expected that the rigorous considerations of this paper are also applicable to these variants.…”

Surface tension effects in the equatorial ocean dynamics

“…The study of wave dynamics in the equatorial region of the Pacific Ocean has attracted the attention of many authors in the recent years, as evidentiated through studies concerning mathematical modeling [2], existence of solutions [3,5,16,18,19,23,24], investigations regarding stability/instability [4,14,17] or even variational formulations [7]. The studies conducted in the mentioned works were stimulated, perhaps, by the peculiar nature of this zone-situated within a band about 2 • latitude from the Equator-manifested through the presence of underlying non-uniform currents, the existence of a diversity of ocean flows and a pronounced stratification.…”

A fixed-point approach for azimuthal equatorial ocean flows

“…On the other hand, they supply the foundations of more direct and relevant analyses by means of asymptotic or perturbative methods. Several recent developments pertaining to geophysical fluid dynamics were obtained by means of investigating exact solutions [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”