In the paper, we present Pollard's exact solution for nonhydrostatic geophysical internal waves with underlying currents in f-plane approximation. We construct the exact solution of nonhydrostatic geophysical internal waves in the presence of underlying currents, extending Pollard's solution to admit underlying horizontal, meridional, and vertical currents at mid-latitudes. Furthermore, we show the underlying meridional and vertical currents are constant. At the equator, the vertical current term vanishes and the meridional current term may vary both zonally and vertically.

Pollard's exact solution for nonhydrostatic geophysical internal waves with underlying currents in f-plane approximation

In this paper, we first present a Pollard's exact solution for geophysical internal waves in equatorial β-plane approximation. Then, we apply the short-wavelength perturbations method to show an instability threshold for geophysical internal waves propagating eastward in the equatorial β-plane approximation.

https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0140293/16681253/026605_1_online.pdf

Pollard's exact solution and instability for geophysical internal waves

An Exact Solution and Instability for Atmospheric Flow in the Modified β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}

Досліджується задача поширення хвиль у тришаровій гідродинамічній системі «шар з твердим дном – шар – шар з кришкою». Для першого наближення отримано дисперсійне співвідношення та дві пари коренів. Отримано вирази відношень амплітуд відхилень поверхонь контакту, які відповідають кореням дисперсійного рівняння. Залежності відношень амплітуд від різних фізичних параметрів графічно проілюстровані та  проаналізовані.

Дослідження хвильових рухів у тришаровій гідродинамічній системі «шар з твердим дном – шар – шар з кришкою»

Exact azimuthal geophysical internal waves with centripetal forces

This paper presents an explicit exact solution of the nonlinear governing equation with Coriolis and centripetal terms in modified equatorial $$\beta $$
 -plane approximation and at arbitrary latitude. The solution describes in the Lagrangian azimuthal equatorially trapped waves propagating eastward in a stratified rotational fluid.

Exact azimuthal equatorially trapped waves with centripetal force in modified equatorial $$\beta $$ β -plane approximation and at arbitrary latitude

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Exact azimuthal equatorially trapped waves with centripetal force in modified equatorial $$\beta $$ β -plane approximation and at arbitrary latitude