Free-surface, purely azimuthal equatorial flows in spherical coordinates with stratification

DOI10.1016/j.jde.2018.11.017zbMath1412.35241OpenAlexW2901158435WikidataQ128887283 ScholiaQ128887283MaRDI QIDQ1731868

David Henry, Calin Iulian Martin

Publication date: 14 March 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.11.017

zbMATH Keywords

Coriolis forceimplicit function theoremspherical coordinatesazimuthal flowsvariable (linear) densityshort-wavelength perturbation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) General theory of rotating fluids (76U05) Free boundary problems for PDEs (35R35) Stability and instability of geophysical and astrophysical flows (76E20) PDEs in connection with geophysics (35Q86) Euler equations (35Q31)

Related Items (26)

Instability of nonlinear wave-current interactions in a modified equatorial \(\beta\)-plane approximation ⋮ On the nonlinear three-dimensional models in equatorial ocean flows ⋮ On three-dimensional free surface water flows with constant vorticity ⋮ Some explicit solutions to the three-dimensional nonlinear water wave problem ⋮ Geophysical water flows with constant vorticity and centripetal terms ⋮ Liouville-type results for the time-dependent three-dimensional (inviscid and viscous) water wave problem with an interface ⋮ A cylindrical coordinates approach concerning azimuthal geophysical flows ⋮ Exact solutions and internal waves for the Antarctic Circumpolar Current in spherical coordinates ⋮ An exact solution representing equatorial wind-drift currents with depth-dependent continuous stratification ⋮ On azimuthally propagating equatorial atmospheric waves ⋮ Modelling the effect of submarine volcanic eruption on equatorial oceanic flows ⋮ Stratified equatorial flows in the \(\beta \)-plane approximation with a free surface ⋮ Stratified periodic water waves with singular density gradients ⋮ Study on a second-order ordinary differential equation for the ocean flow in arctic gyres ⋮ On some azimuthal equatorial flows ⋮ On some azimuthally propagating flows with stratification ⋮ Constant vorticity water flows with full Coriolis term ⋮ Stratified equatorial flows in cylindrical coordinates ⋮ Exact, free-surface equatorial flows with general stratification in spherical coordinates ⋮ A cylindrical coordinates approach concerning the Antarctic Circumpolar Current ⋮ Exponential profiles producing genuine three-dimensional nonlinear flows relevant for equatorial ocean dynamics ⋮ Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates ⋮ An analysis of some exact solutions for stratified wind-stress flows with centripetal effects ⋮ Free surface equatorial flows in spherical coordinates with discontinuous stratification depending on depth and latitude ⋮ Some explicit solutions of the three-dimensional Euler equations with a free surface ⋮ A fixed-point approach for azimuthal equatorial ocean flows

Cites Work

• Instability of equatorially trapped waves in stratified water
• An exact solution for equatorial geophysical water waves with an underlying current
• Local stability for an exact steady purely azimuthal flow which models the antarctic circumpolar current
• Free-surface capillary-gravity azimuthal equatorial flows
• Exact, purely azimuthal stratified equatorial flows in cylindrical coordinates
• Local stability for an exact steady purely azimuthal equatorial flow
• Instability of internal equatorial water waves
• Instability of equatorial water waves with an underlying current
• An exact solution for equatorial waves
• Local stability conditions in fluid dynamics
• Instability criteria for the flow of an inviscid incompressible fluid
• On three-dimensional Gerstner-like equatorial water waves
• On the short-wavelength stabilities of some geophysical flows
• Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography
• Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates
• Equatorially trapped nonlinear water waves in a -plane approximation with centripetal forces
• On the existence of free-surface azimuthal equatorial flows
• Gerstner waves in the presence of mean currents and rotation
• An Explicit Solution for Deep Water Waves With Coriolis Effects
• The dynamics of waves interacting with the Equatorial Undercurrent
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