Equilibration of baroclinic instability in westward flows

Author(s):  
Timour Radko ◽  
James C. McWilliams ◽  
Georgi G. Sutyrin

AbstractWe explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasi-geostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.

2009 ◽  
Vol 26 (7) ◽  
pp. 074704 ◽  
Author(s):  
Wang Li-Feng ◽  
Ye Wen-Hua ◽  
Fan Zheng-Feng ◽  
Xue Chuang ◽  
Li Ying-Jun

1995 ◽  
Vol 291 ◽  
pp. 109-138 ◽  
Author(s):  
Michael D. Mundt ◽  
Nicholas H. Brummell ◽  
John E. Hart

The behaviour of baroclinic waves growing from instability in a two-layer channel flow with rigid (no-slip) sidewalls is described and contrasted with that for the more traditional free-slip boundary conditions. The linear theory for the onset of small-amplitude disturbances shows that the change in lateral boundary conditions has only a modest effect for typical laboratory parameter values, although the no-slip case is slightly more unstable at very small values of bottom friction. On the other hand, the nonlinear evolution of no-slip modes is completely different. While the free-slip case becomes aperiodic only at large values of the supercriticality (F–Fc)/Fc, the rigid wall case can be subcritically chaotic. Aperiodic, highly nonlinear wave motions are possible for external control values set in the linearly stable region of parameter space. Weakly nonlinear analysis shows that the no-slip case has a negative Landau constant for moderately small values of bottom friction, and it is in this regime that high-resolution numerical simulations exhibit subcritical chaos. At larger values of bottom friction, the rigid-wall simulations undergo a supercritical quasi-periodic transition to chaos at modest, order one, supercriticality, which is substantially smaller than that required for chaos in the free-slip case.


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