Instability of Equatorial Water Waves with an Underlying Current

Abstract

Abstract. In this paper we use the short-wavelength instability approach to derive an instability threshold for exact trapped equatorial waves propagating eastwards in the presence of an underlying current.

Hamiltonian approach to the modeling of internal geophysical waves with vorticity

“…Further to the obtained results, non-linear eects and non-linear model equations need to be studied, like in [15], [18], [19], [25], etc. The problem of instability of the waves, as recently pursued in the publications [26], [27], [28] would be of interest.…”

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.…”