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Introduction to PDEs and waves for the atmosphere and ocean
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In this article, some remarkable features of stratified flow are discussed, including linear and nonlinear instability of strongly stratified flows with strong stratification Rotating shallow water theory Linear and weakly nonlinear theory of dispersive waves with geophysical examples Simplified equations for the dynamics of strongly-strained flow The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations.Abstract:
Introduction Some remarkable features of stratified flow Linear and nonlinear instability of stratified flows with strong stratification Rotating shallow water theory Linear and weakly nonlinear theory of dispersive waves with geophysical examples Simplified equations for the dynamics of strongly stratified flow The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations Introduction to averaging over fast waves for geophysical flows Waves and PDEs for the equatorial atmosphere and ocean Bibliography.read more
Citations
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Journal ArticleDOI
Global regularity for the 2D Boussinesq equations with partial viscosity terms
TL;DR: In this article, Ricca et al. proved the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity.
Journal ArticleDOI
The skeleton of tropical intraseasonal oscillations
TL;DR: A minimal dynamical model for the Madden–Julian oscillation that recovers robustly its fundamental features on intraseasonal/planetary scales and drives the “skeleton” of the MJO through modulated heating.
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Filtering Complex Turbulent Systems
Andrew J. Majda,John Harlim +1 more
TL;DR: In this paper, the authors present mathematical strategies for filtering turbulent signal with model error, including the Kalman filter for vector systems, reduced filters and a three-dimensional toy model.
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Waves and Mean Flows
TL;DR: In this paper, a detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave-mean interaction theory, and the author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows.