Inertial, barotropic, and baroclinic instabilities of the Bickley jet in two-layer rotating shallow water model

2011 ◽  
Vol 23 (12) ◽  
pp. 126601 ◽  
Author(s):  
François Bouchut ◽  
Bruno Ribstein ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model ◽  
Rotating Shallow Water

Instabilities of coupled density fronts and their nonlinear evolution in the two-layer rotating shallow-water model: influence of the lower layer and of the topography

2013 ◽  
Vol 716 ◽  
pp. 528-565 ◽  
Author(s):  
Bruno Ribstein ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Nonlinear Evolution ◽  
Lower Layer ◽  
Phase Locking ◽  
Water Model ◽  
Shallow Water Model ◽  
Wave Instability ◽  
Rotating Shallow Water ◽  
New Generation ◽  
Rotating Shallow Water Equations

AbstractWe undertake a detailed analysis of linear stability of geostrophically balanced double density fronts in the framework of the two-layer rotating shallow-water model on the $f$-plane with topography, the latter being represented by an escarpment beneath the fronts. We use the pseudospectral collocation method to identify and quantify different kinds of instabilities resulting from phase locking and resonances of frontal, Rossby, Poincaré and topographic waves. A swap in the leading long-wave instability from the classical barotropic form, resulting from the resonance of two frontal waves, to a baroclinic form, resulting from the resonance of Rossby and frontal waves, takes place with decreasing depth of the lower layer. Nonlinear development and saturation of these instabilities, and of an instability of topographic origin, resulting from the resonance of frontal and topographic waves, are studied and compared with the help of a new-generation well-balanced finite-volume code for multilayer rotating shallow-water equations. The results of the saturation for different instabilities are shown to produce very different secondary coherent structures. The influence of the topography on these processes is highlighted.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

Rotating Shallow-Water model with Horizontal Density and/or Temperature Gradients

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Potential Temperature ◽  
Wave Spectrum ◽  
Water Model ◽  
Strong Mixing ◽  
Shallow Water Model ◽  
New Class ◽  
Centrifugal Instability ◽  
Rotating Shallow Water ◽  
Specific Equation

The derivation of rotating shallow-water equations by vertical averaging and columnar motion hypothesis is repeated without supposing horizontal homogeneity of density/potential temperature. The so-called thermal rotating shallow-water model arises as the result. The model turns to be equivalent to gas dynamics with a specific equation of state. It is shown that it possesses Hamiltonian structure and can be derived from a variational principle. Its solution at low Rossby numbers should obey the thermo-geostrophic equilibrium, replacing the standard geostrophic equilibrium. The wave spectrum of the model is analysed, and the appearance of a whole new class of vortex instabilities of convective type, resembling asymmetric centrifugal instability and leading to a strong mixing at nonlinear stage, is demonstrated.

Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Variational Principles ◽  
Mean Field ◽  
Tangent Plane ◽  
Primitive Equations ◽  
Water Model ◽  
Shallow Water Model ◽  
Shallow Water Models ◽  
Rotating Shallow Water

In this chapter, one- and two-layer versions of the rotating shallow-water model on the tangent plane to the rotating, and on the whole rotating sphere, are derived from primitive equations by vertical averaging and columnar motion (mean-field) hypothesis. Main properties of the models including conservation laws and wave-vortex dichotomy are established. Potential vorticity conservation is derived, and the properties of inertia–gravity waves are exhibited. The model is then reformulated in Lagrangian coordinates, variational principles for its one- and two-layer version are established, and conservation laws are reinterpreted in these terms.

Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

2012 ◽  
Vol 706 ◽  
pp. 71-107 ◽  
Author(s):  
Noé Lahaye ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Coherent Structures ◽  
Water Model ◽  
Shallow Water Model ◽  
Scatter Plot ◽  
Weak Stratification ◽  
Rotating Shallow Water ◽  
Frontal Collisions ◽  
Inertia Gravity Waves

AbstractWe study formation and properties of new coherent structures: ageostrophic modons in the two-layer rotating shallow water model. The ageostrophic modons are obtained by ‘ageostrophic adjustment’ of the exact modon solutions of the two-layer quasi-geostrophic equations with the free surface, which are used to initialize the full two-layer shallow water model. Numerical simulations are performed using a well-balanced high-resolution finite volume numerical scheme. For large enough Rossby numbers, the initial configurations undergo ageostrophic adjustment towards asymmetric ageostrophic quasi-stationary coherent dipoles. This process is accompanied by substantial emission of inertia–gravity waves. The resulting dipole is shown to be robust and survives frontal collisions. It contains captured inertia–gravity waves and, for higher Rossby numbers and weak stratification, carries a (baroclinic) hydraulic jump at its axis. For stronger stratifications and high enough Rossby numbers, ‘rider’ coherent structures appear as a result of adjustment, with a monopole in one layer and a dipole in another. Other ageostrophic coherent structures, such as two-layer tripoles and two-layer modons with nonlinear scatter plot, result from the collisions of ageostrophic modons. They are shown to be long-living and robust, and to capture waves.

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