Vortex rigid motion in quasi-geostrophic shallow-water equations

A ‘‘vortex in cell” model for quasi-geostrophic, shallow water dynamics on the sphere

Article history: Received 15 July 2009 Received in revised form 29 December 2009 Accepted 4 January 2010 Available online 1 February 2010

New Developments and Cosine Effect in the Viscous Shallow Water and Quasi-geostrophic Equations

The viscous Shallow Water Equations and Quasi-Geostrophic Equations are considered in this paper. Some new terms, related to the Coriolis force, are revealed thanks to a rigorous asymptotic analysis. After providing well-posedness arguments for the new models, the authors perform some numerical computations that confirm the role played by the cosine effect in various physical configurations. Ke...

Precipitating Quasi-Geostrophic Equations and Potential Vorticity

Precipitating versions of the quasi-geostrophic (QG) equations are derived systematically, starting from the equations of a cloud-resolving model. The presence of phase changes of water from vapor to liquid and vice versa leads to important differences from the dry QG case. The precipitating QG (PQG) equations, in their simplest form, have two variables to describe the full system: a potential ...

Dissipative quasi - geostrophic equations with initial data

In this paper, we study the solutions of the initial-value problem (IVP) for the quasi-geostrophic equations, namely ∂tθ + u.∇θ + κ (−∆) θ = 0, on R × ]0,+∞[ , θ (x, 0) = θ0(x), x ∈ R. Our goal is to establish the existence and uniqueness of regulars solutions for the two-dimentional dissipative quasi-geostrophic equation with initial data in a Sobolev space H satisfying suitable conditions wit...

Wavenumber-frequency analysis of single-layer shallow-water beta-plane quasi- geostrophic turbulence