Instability of equatorial water waves in the \(f\)-plane
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Publication:477383
DOI10.3934/dcds.2015.35.909zbMath1304.35698OpenAlexW2315996561MaRDI QIDQ477383
Publication date: 3 December 2014
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2015.35.909
PDEs in connection with fluid mechanics (35Q35) Vortex flows for incompressible inviscid fluids (76B47) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) General theory of rotating fluids (76U05) Almost and pseudo-almost periodic solutions to PDEs (35B15) Stability and instability of geophysical and astrophysical flows (76E20) PDEs in connection with geophysics (35Q86)
Related Items (36)
Hamiltonian approach to the modeling of internal geophysical waves with vorticity ⋮ Exact and explicit internal equatorial water waves with underlying currents ⋮ The dynamics of flat surface internal geophysical waves with currents ⋮ Variational formulations of steady rotational equatorial waves ⋮ Exact solution and instability for geophysical waves with centripetal forces and at arbitrary latitude ⋮ Instability of equatorial edge waves in the background flow ⋮ Equatorial water waves with underlying currents in the f-plane approximation ⋮ Hamiltonian model for coupled surface and internal waves in the presence of currents ⋮ Global diffeomorphism of the Lagrangian flow-map for equatorially-trapped internal water waves ⋮ On three-dimensional Gerstner-like equatorial water waves ⋮ A harmonic maps approach to fluid flows ⋮ Steady periodic waves and formal stability for fixed-depth rotational equatorial flows ⋮ Exact equatorial water waves in the \(f\)-plane ⋮ Stability properties of nontrivial periodic water waves for fixed-depth rotational equatorial flows ⋮ The global bifurcation and geometric properties of steady periodic equatorial internal waves with fixed-depth ⋮ A cylindrical coordinates approach to constant vorticity geophysical waves with centripetal forces at arbitrary latitude ⋮ Stratified equatorial flows in cylindrical coordinates ⋮ Global diffeomorphism of the Lagrangian flow-map defining equatorially trapped water waves ⋮ Local stability for an exact steady purely azimuthal equatorial flow ⋮ A Hamiltonian approach for nonlinear rotational capillary-gravity water waves in stratified flows ⋮ Instability of geophysical flows at arbitrary latitude ⋮ Periodic equatorial water flows from a Hamiltonian perspective ⋮ Surface tension effects in the equatorial ocean dynamics ⋮ Azimuthal equatorial capillary-gravity flows in spherical coordinates ⋮ Mean flow velocities and mass transport for equatorially-trapped water waves with an underlying current ⋮ Exact azimuthal internal waves with an underlying current ⋮ Instability of internal equatorial water waves ⋮ Local stability for an exact steady purely azimuthal flow which models the antarctic circumpolar current ⋮ On the trigonometric polynomial Ansatz for gravity water waves ⋮ Free-surface capillary-gravity azimuthal equatorial flows ⋮ An exact solution for geophysical internal waves with underlying current in modified equatorial β-plane approximation* ⋮ Exact solution and instability for geophysical waves in modified equatorial \(\beta\)-plane approximation with and without centripetal forces ⋮ Internal equatorial water waves in the f−plane ⋮ Dynamics of the thermocline in the equatorial region of the Pacific ocean ⋮ On the existence of free-surface azimuthal equatorial flows ⋮ On the existence of solutions and the pressure function related to the antarctic circumpolar current
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