Averaging over fast gravity waves for geophysical flows with arbitary

DOI10.1080/03605309608821200zbMath0849.35106OpenAlexW1993762544MaRDI QIDQ4881620

Publication date: 14 November 1996

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309608821200

zbMATH Keywords

Boussinesq equation quasi-geostrophic equations rotating shallow water equations gravity wave vortical waves quasi-geostrophic limit large scale geophysical flows in the atmosphere and ocean

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05)

Related Items (65)

Near-resonance approximation of rotating Navier–Stokes equations ⋮ Low Rossby limiting dynamics for stably stratified flow with finite Froude number ⋮ Singular limits of the Cauchy problem to the two-layer rotating shallow water equations ⋮ On the regularization mechanism for the periodic Korteweg-de Vries equation ⋮ Asymptotics and lower bound for the lifespan of solutions to the primitive equations ⋮ ON THE REGULARITY OF THREE-DIMENSIONAL ROTATING EULER–BOUSSINESQ EQUATIONS ⋮ 3D stochastic primitive equations of the large-scale ocean: Global well-posedness and attractors ⋮ On the effect of fast rotation and vertical viscosity on the lifespan of the \(3D\) Primitive equations ⋮ Averaging method applied to the three-dimensional primitive equations ⋮ Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers ⋮ Rotation prevents finite-time breakdown ⋮ Fast and slow resonant triads in the two-layer rotating shallow water equations ⋮ A posteriori error estimates for viscous flow problems with rotation ⋮ Averaging principle for stochastic quasi‐geostrophic flow equation with a fast oscillation ⋮ Quasigeostrophic equation with random initial data in negative-order Sobolev space ⋮ Reduction methods in climate dynamics -- a brief review ⋮ On the wave turbulence theory for stratified flows in the ocean ⋮ Ekman layers of rotating fluids, the case of well prepared initial data ⋮ Unnamed Item ⋮ Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence ⋮ Unnamed Item ⋮ Initial investigations of precipitating quasi-geostrophic turbulence with phase changes ⋮ New intermediate models for rotating shallow water and an investigation of the preference for anticyclones ⋮ Dynamics of turbulence strongly influenced by buoyancy ⋮ A two-grid finite difference method for the primitive equations of the ocean ⋮ Homogenization of Hamiltonian systems with a strong constraining potential ⋮ Three-scale singular limits of the rotating stratified Boussinesq equations ⋮ Finite dimensionality of global attractor for the solutions to 3D viscous primitive equations of large-scale moist atmosphere ⋮ Weak convergence results for inhomogeneous rotating fluid equations ⋮ Global existence for the primitive equations with small anisotropic viscosity ⋮ Fast averaging for long- and short-wave scaled equatorial shallow water equations with Coriolis parameter deviating from linearity ⋮ Existence of the universal attractor for the 3-D viscous primitive equations of large-scale moist atmosphere ⋮ Asymptotics and vortex patches for the quasigeostrophic approximation ⋮ Renormalization group method applied to the primitive equations ⋮ Finite-time blowup and ill-posedness in Sobolev spaces of the inviscid primitive equations with rotation ⋮ Global Well-Posedness and Asymptotics for a Geophysical Fluid System ⋮ Weakly nonlinear-dissipative approximations of hyperbolic-parabolic systems with entropy ⋮ Fast Wave Averaging for the Equatorial Shallow Water Equations ⋮ Fast-wave averaging with phase changes: asymptotics and application to moist atmospheric dynamics ⋮ Model dynamics and vertical collapse in decaying strongly stratified flows ⋮ Low Froude and Rossby number three-scale singular limits of the rotating stratified Boussinesq equations ⋮ On the order of magnitude of the baroclinic flow in the primitive equations of the ocean ⋮ A simple justification of the singular limit for equatorial shallow‐water dynamics ⋮ Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics ⋮ Wave adjustment: general concept and examples ⋮ Balanced and unbalanced components of moist atmospheric flows with phase changes ⋮ Global well-posedness for the primitive equations with less regular initial data ⋮ Effects of clouds and phase changes on fast-wave averaging: a numerical assessment ⋮ The multilayer shallow water system in the limit of small density contrast ⋮ Investigations of non-hydrostatic, stably stratified and rapidly rotating flows ⋮ Dissipative quasi-geostrophic dynamics under random forcing ⋮ Asymptotic of the solutions of hyperbolic equations with a skew-symmetric perturbation ⋮ On viscous shallow water equations (Saint-Venant model) and the quasi-geostrophic limit ⋮ Applications of Schochet's methods to parabolic equations ⋮ On the effect of rotation on the life-span of analytic solutions to the \(3D\) Inviscid primitive equations ⋮ A remark on the three-dimensional baroclinic quasi-geostrophic dynamics ⋮ On mathematical problems for the primitive equations of the ocean: The mesoscale midlatitude case ⋮ Parareal Convergence for Oscillatory PDEs with Finite Time-Scale Separation ⋮ Time-periodic quasigeostrophic motion under dissipation and forcing ⋮ On regularity of solutions of 3D navier-stokes equations ⋮ Mathematical analysis of geophysical balance models ⋮ Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics ⋮ Noisy Lagrangian tracers for filtering random rotating compressible flows ⋮ Vortical and wave modes in 3D rotating stratified flows: random large-scale forcing ⋮ Near resonant approximation of the rotating stratified Boussinesq system on a 3-torus

Cites Work

This page was built for publication: Averaging over fast gravity waves for geophysical flows with arbitary