Baroclinic instability of quasi-geostrophic flows localized in a thin layer

1995 ◽  
Vol 288 ◽  
pp. 175-199 ◽  
Author(s):  
E. S. Benilov
Keyword(s):  
Baroclinic Instability ◽  
Vertical Shear ◽  
Layer Model ◽  
Effective Time ◽  
Sufficient Stability ◽  
Geostrophic Flows ◽  
Characteristic Spatial Scale ◽  
Northern Pacific ◽  
Two Layer Model ◽  
Layer I

This paper examines the baroclinic instability of a quasi-geostrophic flow with vertical shear in a continuously stratified fluid. The flow and density stratification are both localized in a thin upper layer. (i) Disturbances whose wavelength is much smaller than the deformation radius (based on the depth of the upper layer) are demonstrated to satisfy an ‘equivalent two-layer model’ with properly chosen parameters. (ii) For disturbances whose wavelength is of the order of, or greater than, the deformation radius we derive a sufficient stability criterion. The above analysis is applied to the subtropical and subarctic frontal currents in the Northern Pacific. The effective time of growth of disturbances (i) is found to be 16–22 days, the characteristic spatial scale is 130–150 km.

On the Thickness Ratio in the Quasigeostrophic Two-Layer Model of Baroclinic Instability

2013 ◽  
Vol 70 (5) ◽  
pp. 1505-1511 ◽  
Author(s):  
Noboru Nakamura ◽  
Lei Wang
Keyword(s):  
Growth Rate ◽  
Vertical Structure ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Thickness Ratio ◽  
Layer Model ◽  
Optimal Thickness ◽  
Zonal Wavenumber ◽  
The Mean ◽  
Two Layer Model

Abstract It is shown that the classical quasigeostrophic two-layer model of baroclinic instability possesses an optimal ratio of layer thicknesses that maximizes the growth rate, given the basic-state shear (thermal wind), beta, and the mean Rossby radius. This ratio is interpreted as the vertical structure of the most unstable mode. For positive shear and beta, the optimal thickness of the lower layer approaches the midheight of the model in the limit of strong criticality (shear/beta) but it is proportional to criticality in the opposite limit. For a set of parameters typical of the earth’s midlatitudes, the growth rate maximizes at a lower-layer thickness substantially less than the midheight and at a correspondingly larger zonal wavenumber. It is demonstrated that a turbulent baroclinic jet whose statistical steady state is marginally critical when run with equal layer thicknesses can remain highly supercritical when run with a nearly optimal thickness ratio.

Instability of a solid-body rotating vortex in a two-layer model

1992 ◽  
Vol 242 ◽  
pp. 395-417 ◽  
Author(s):  
P. Ripa
Keyword(s):  
Solid Body ◽  
Rotation Rate ◽  
Baroclinic Instability ◽  
Dynamic Structure ◽  
Pressure Force ◽  
Integrals Of Motion ◽  
Layer Model ◽  
Unperturbed State ◽  
Relative Thickness ◽  
Two Layer Model

The instability of an anticyclonic solid-body rotating eddy embedded on a quiescent environment is studied, for all possible values of the parameters of the unperturbed state, i.e. the vortex's relative thickness and rotation rate. The Coriolis force is fundamental for the existence of the eddy (because the pressure force has a centrifugal direction) and therefore this analysis pertains to the study of mesoscale vortices in the ocean or the atmosphere, as well as those in other planets.These eddies are known to be stable when the ‘second’ layer is assumed imperturbable (infinitely deep); however, here these vortices are found to be unstable in the more realistic case of an active environment layer, which may be arbitrarily thick.Three basic types of instability are found, classified according to the dynamic structure of the growing perturbation field, in both layers: baroclinic instability (Rossby-like in both layers), Sakai instability (Poincaré-like in the vortex layer and Rossby-like in the environment), and Kelvin–Helmholtz instability (Poincaré-like in both layers). In addition, there is a hybrid instability, which goes continuously from the baroclinic to the Sakai types, as the rotation rate is increased.The problem is constrained by the conservation of pseudoenergy and angular pseudomomentum, which are quadratic (to lowest order) in the perturbation. The requirement that both integrals of motion vanish for a growing disturbance, determines the structure of the latter in both layers. Furthermore, that constraint restricts the region, in parameter space, where each type of instability is present.

scholarly journals The Influence of Stratification on the Instabilities in an Idealized Two-Layer Ocean Model

2014 ◽  
Vol 44 (10) ◽  
pp. 2718-2738 ◽  
Author(s):  
R. L. Irwin ◽  
F. J. Poulin
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Nonlinear Evolution ◽  
Ocean Model ◽  
Vertical Shear ◽  
General Context ◽  
Layer Model ◽  
Different Types ◽  
Two Layer Model ◽  
Rotating Shallow Water

Abstract This work investigates the instability of a two-layer Bickley jet in the context of the rotating shallow water (RSW) model. This provides a general context in which the instability of oceanographic jets with simple stratification can be investigated. The three objectives of this work are as follows: First, the study investigates the morphology of unstable modes that can occur in this two-layer model. This is done by performing a linear stability analysis to investigate different types of flows both with and without vertical shear. Second, the authors study how the growth rates of the unstable modes are affected by changes in the stratification. Third, this study looks at the nonlinear evolution of some of these instabilities to determine how easy it is for nonprimary instabilities to develop. This is motivated by the fact that in the literature there have been many investigations that have found a multitude of unstable modes in this model, and it is not evident as to how easily they can be generated in oceanographic flows.

scholarly journals Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

2015 ◽  
Vol 785 ◽  
pp. 1-30 ◽  
Author(s):  
Jean N. Reinaud ◽  
Xavier Carton
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Steady States ◽  
Point Vortices ◽  
Velocity Shear ◽  
Vertical Shear ◽  
Finite Area ◽  
Geostrophic Flows ◽  
Vertically Aligned ◽  
Baroclinic Vortices

Hetons are baroclinic vortices able to transport tracers or species, which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. First, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-of-eight shaped) upper cores. In the case of vertically distant upper and lower cores, the latter can nearly join near the centre of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.

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