Nonlinear saturation of baroclinic instability in the generalized Phillips model (I) —The upper bound on the evolution of disturbance to the nonlinearly unstable basic flow

2002 ◽  
Vol 23 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Zhang Gui ◽  
Xiang Jie ◽  
Li Dong-hui
Keyword(s):  
Upper Bound ◽  
Baroclinic Instability ◽  
Basic Flow ◽  
Nonlinear Saturation ◽  
Phillips Model ◽  
Generalized Phillips Model

Instabilities of Jets and Fronts and their Nonlinear Evolution

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Trapped Modes ◽  
Nonlinear Saturation ◽  
Parallel Flows ◽  
Inertial Instability ◽  
Shear Instabilities ◽  
Linear And Nonlinear ◽  
Flow Configurations ◽  
Characteristic Features

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

Ageostrophic instabilities of fronts in a channel in a stratified rotating fluid

2009 ◽  
Vol 627 ◽  
pp. 485-507 ◽  
Author(s):  
J. GULA ◽  
R. PLOUGONVEN ◽  
V. ZEITLIN
Keyword(s):  
Baroclinic Instability ◽  
Water Model ◽  
Small Scale ◽  
Rotating Fluid ◽  
Shallow Water Model ◽  
Mean Flow ◽  
Nonlinear Saturation ◽  
The Mean ◽  
Rotating Shallow Water ◽  
Stability Results

It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby–Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149–176) in a two-layer rotating shallow-water model. First, we benchmark our method by reproducing the linear stability results obtained by Sakai (1989) and extend them to more general configurations. Second, in order to determine the relevance of RK instability in more realistic flows, simulations of the evolution of a front in a continuously stratified fluid are carried out. They confirm the presence of RK instability with characteristics comparable to those found in the two-layer case. Finally, these simulations are used to study the nonlinear saturation of the RK modes. It is shown that saturation is achieved through the development of small-scale instabilities along the front which modify the mean flow so as to stabilize the RK mode. Remarkably, the developing instability leads to conversion of kinetic energy of the basic flow to potential energy, contrary to classical baroclinic instability.

Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid

2014 ◽  
Vol 743 ◽  
pp. 1-31 ◽  
Author(s):  
Bruno Ribstein ◽  
Riwal Plougonven ◽  
Vladimir Zeitlin
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Large Range ◽  
Baroclinic Instability ◽  
Forecast Model ◽  
Rotating Fluid ◽  
Nonlinear Saturation ◽  
Unstable Region ◽  
Long Wave ◽  
Inertial Instability

AbstractThe paper contains a detailed study of the inertial instability of a barotropic Bickley jet on the $f$-plane in the continuously stratified primitive equations model, and a comparison of this essentially ageostrophic instability with the classical baroclinic one. Analytical and numerical investigation of the linear stability of the jet in the long-wave sector is performed for a range of Rossby and Burger numbers. The major results are that: (1) the standard symmetric inertial instability, appearing at high enough Rossby numbers, turns out to be the infinite-wavelength limit of an asymmetric inertial instability, this latter having the highest growth rate for a large range of vertical wavenumbers; (2) inertial instability coexists with the standard baroclinic instability, which becomes dominant at small Rossby numbers. Nonlinear saturation of the inertial instability of the jet with a superimposed random small-amplitude perturbation is then studied, using the Weather Research and Forecast model. It is shown that at first stages the inertial instability dominates. It is localized near the maximum of the anticyclonic shear and is associated with the highest attainable value of the vertical wavenumber. The saturation of the inertial instability leads to the homogenization of the geostrophic momentum in the unstable region. At later stages, another baroclinic instability develops, characterized by lower values of the vertical wavenumber. This instability saturates by forming large-scale vortices downstream. It is identified as the leading instability of a marginally inertially stable jet resulting from the initial one through homogenization of the geostrophic momentum. The rough scenario of the evolution of essentially ageostrophic jets is, thus, as follows: the inertial instability rapidly saturates and baroclinic instability takes over. It is shown that reorganization of the flow due to developing instabilities is an efficient source of inertia-gravity waves.

Modal Interpretation for the Ekman Destabilization of Inviscidly Stable Baroclinic Flow in the Phillips Model

2010 ◽  
Vol 40 (4) ◽  
pp. 830-839 ◽  
Author(s):  
Gordon E. Swaters
Keyword(s):  
Phase Velocity ◽  
Boundary Layers ◽  
Rossby Wave ◽  
Classical Theory ◽  
Baroclinic Instability ◽  
Ekman Layer ◽  
Modal Interpretation ◽  
Phase Velocities ◽  
Phillips Model ◽  
Baroclinic Flow

Abstract Ekman boundary layers can lead to the destabilization of baroclinic flow in the Phillips model that, in the absence of dissipation, is nonlinearly stable in the sense of Liapunov. It is shown that the Ekman-induced instability of inviscidly stable baroclinic flow in the Phillips model occurs if and only if the kinematic phase velocity associated with the dissipation lies outside the interval bounded by the greatest and least neutrally stable Rossby wave phase velocities. Thus, Ekman-induced destabilization does not correspond to a coalescence of the barotropic and baroclinic Rossby modes as in classical inviscid baroclinic instability. The differing modal mechanisms between the two instability processes is the reason why subcritical baroclinic shears in the classical theory can be destabilized by an Ekman layer, even in the zero dissipation limit of the theory.

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