Steady radiating baroclinic vortices in vertically sheared flows

2021 ◽  
Author(s):  
Georgi Sutyrin ◽  
Jonas Nycander ◽  
Timour Radko
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Vertical Shear ◽  
Alternative Mechanism ◽  
Beta Plane ◽  
Subtropical Oceans ◽  
Baroclinic Vortices ◽  
Favorable Conditions

<p>Baroclinic vortices embedded in a large-scale vertical shear are examined. We describe a new class of steady propagating vortices that radiate Rossby waves but yet do not decay. This is possible since they can extract available potential energy (APE) from a large-scale vertically sheared flow, even though this flow is linearly stable. The vortices generate Rossby waves which induce a meridional vortex drift and an associated heat flux explained by an analysis of pseudomomentum and pseudoenergy. An analytical steady solution is considered for a marginally stable flow in a two-layer model on the beta-plane, where the beta-effect is compensated by the potential vorticity gradient (PVG) associated with the meridional slope of the density interface. The compensation occurs in the upper layer for an upper layer westward flow (an easterly shear) and in the lower layer for an upper layer eastward flow (the westerly shear). The theory is confirmed by numerical simulations indicating that for westward flows in subtropical oceans, the reduced PVG in the upper layer provides favorable conditions for eddy persistence and long-range propagation. The drifting and radiating vortex is an alternative mechanism besides baroclinic instability for converting background APE to mesoscale energy. </p>

scholarly journals Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

2014 ◽  
Vol 44 (7) ◽  
pp. 1919-1940 ◽  
Author(s):  
T. Radko ◽  
D. Peixoto de Carvalho ◽  
J. Flanagan
Keyword(s):  
Numerical Simulations ◽  
Large Scale ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Vertical Shear ◽  
Balance Model ◽  
Mesoscale Variability ◽  
Beta Effect ◽  
Eddy Transport ◽  
Secondary Instabilities

Abstract A theoretical model is developed, which attempts to predict the lateral transport by mesoscale variability, generated and maintained by baroclinic instability of large-scale flows. The authors are particularly concerned by the role of secondary instabilities of primary baroclinically unstable modes in the saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for evaluating the equilibrium magnitude of mesoscale eddies as a function of the background parameters: vertical shear, stratification, beta effect, and bottom drag. The proposed technique is applied to two classical models of baroclinic instability—the Phillips two-layer model and the linearly stratified Eady model. Theory predicts that the eddy-driven lateral mixing rapidly intensifies with increasing shear and weakens when the beta effect is increased. The eddy transport is also sensitive to the stratification pattern, decreasing as the ratio of upper/lower layer depths in the Phillips model is decreased below unity. Theory is successfully tested by a series of direct numerical simulations that span a wide parameter range relevant for typical large-scale currents in the ocean. The spontaneous emergence of large-scale patterns induced by mesoscale variability, and their role in the cross-flow eddy transport, is examined using a suite of numerical simulations.

Getting Rid of Fast Waves: Slow Dynamics

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Rossby Waves ◽  
Baroclinic Instability ◽  
Nonlinear Effects ◽  
Kelvin Wave ◽  
Beta Plane ◽  
Equatorial Wave ◽  
Flow Over Topography ◽  
Wave Guides ◽  
Rotating Shallow Water ◽  
Fast Waves

After analysis of general properties of horizontal motion in primitive equations and introduction of principal parameters, the key notion of geostrophic equilibrium is introduced. Quasi-geostrophic reductions of one- and two-layer rotating shallow-water models are obtained by a direct filtering of fast inertia–gravity waves through a choice of the time scale of motions of interest, and by asymptotic expansions in Rossby number. Properties of quasi-geostrophic models are established. It is shown that in the beta-plane approximations the models describe Rossby waves. The first idea of the classical baroclinic instability is given, and its relation to Rossby waves is explained. Modifications of quasi-geostrophic dynamics in the presence of coastal, topographic, and equatorial wave-guides are analysed. Emission of mountain Rossby waves by a flow over topography is demonstrated. The phenomena of Kelvin wave breaking, and of soliton formation by long equatorial and topographic Rossby waves due to nonlinear effects are explained.

scholarly journals The Loop Current: Observations of Deep Eddies and Topographic Waves

2019 ◽  
Vol 49 (6) ◽  
pp. 1463-1483 ◽  
Author(s):  
Peter Hamilton ◽  
Amy Bower ◽  
Heather Furey ◽  
Robert Leben ◽  
Paula Pérez-Brunius
Keyword(s):  
Large Scale ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Short Interval ◽  
Loop Current ◽  
Boundary Current ◽  
The West ◽  
Eastern Basin ◽  
Topographic Rossby Waves ◽  
Deep Eddies

AbstractA set of float trajectories, deployed at 1500- and 2500-m depths throughout the deep Gulf of Mexico from 2011 to 2015, are analyzed for mesoscale processes under the Loop Current (LC). In the eastern basin, December 2012–June 2014 had >40 floats per month, which was of sufficient density to allow capturing detailed flow patterns of deep eddies and topographic Rossby waves (TRWs), while two LC eddies formed and separated. A northward advance of the LC front compresses the lower water column and generates an anticyclone. For an extended LC, baroclinic instability eddies (of both signs) develop under the southward-propagating large-scale meanders of the upper-layer jet, resulting in a transfer of eddy kinetic energy (EKE) to the lower layer. The increase in lower-layer EKE occurs only over a few months during meander activity and LC eddy detachment events, a relatively short interval compared with the LC intrusion cycle. Deep EKE of these eddies is dispersed to the west and northwest through radiating TRWs, of which examples were found to the west of the LC. Because of this radiation of EKE, the lower layer of the eastern basin becomes relatively quiescent, particularly in the northeastern basin, when the LC is retracted and a LC eddy has departed. A mean west-to-east, anticyclone–cyclone dipole flow under a mean LC was directly comparable to similar results from a previous moored LC array and also showed connections to an anticlockwise boundary current in the southeastern basin.

Overtransmission of Rossby Waves at a Lower-Layer Critical Latitude in the Two-Layer Model

2020 ◽  
Vol 77 (3) ◽  
pp. 859-870 ◽  
Author(s):  
Matthew T. Gliatto ◽  
Isaac M. Held
Keyword(s):  
Rossby Waves ◽  
Lower Layer ◽  
Scattering Problem ◽  
Lower Troposphere ◽  
Vertical Shear ◽  
Mean Flow ◽  
External Mode ◽  
The Mean ◽  
Critical Latitude ◽  
Pv Gradient

Abstract Rossby waves, propagating from the midlatitudes toward the tropics, are typically absorbed by critical latitudes (CLs) in the upper troposphere. However, these waves typically encounter CLs in the lower troposphere first. We study a two-layer linear scattering problem to examine the effects of lower CLs on these waves. We begin with a review of the simpler barotropic case to orient the reader. We then progress to the baroclinic case using a two-layer quasigeostrophic model in which there is vertical shear in the mean flow on which the waves propagate, and in which the incident wave is assumed to be an external-mode Rossby wave. We use linearized equations and add small damping to remove the critical-latitude singularities. We consider cases in which either there is only one CL, in the lower layer, or there are CLs in both layers, with the lower-layer CL encountered first. If there is only a CL in the lower layer, the wave’s response depends on the sign of the mean potential vorticity gradient at this lower-layer CL: if the PV gradient is positive, then the CL partially absorbs the wave, as in the barotropic case, while for a negative PV gradient, the CL is a wave emitter, and can potentially produce overreflection and/or overtransmission. Our numerical results indicate that overtransmission is by far the dominant response in these cases. When an upper-layer absorbing CL is encountered, following the lower-layer encounter, one can still see the signature of overtransmission at the lower-layer CL.

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.

scholarly journals On the Poleward Motion of Midlatitude Cyclones in a Baroclinic Meandering Jet

2013 ◽  
Vol 70 (8) ◽  
pp. 2629-2649 ◽  
Author(s):  
Ludivine Oruba ◽  
Guillaume Lapeyre ◽  
Gwendal Rivière
Keyword(s):  
Potential Vorticity ◽  
Statistical Study ◽  
Rossby Waves ◽  
Lower Layer ◽  
Finite Amplitude ◽  
Synoptic Scale ◽  
Beta Plane ◽  
The Cross ◽  
Quasigeostrophic Model ◽  
Pv Gradient

Abstract The motion of surface depressions evolving in a background meandering baroclinic jet is investigated using a two-layer quasigeostrophic model on a beta plane. Synoptic-scale finite-amplitude cyclones are initialized in the lower and upper layer to the south of the jet in a configuration favorable to their baroclinic interaction. The lower-layer cyclone is shown to move across the jet axis from its warm-air to cold-air side. It is the presence of a poleward-oriented barotropic potential vorticity (PV) gradient that makes possible the cross-jet motion through the beta-drift mechanism generalized to a baroclinic atmospheric context. The potential vorticity gradient associated with the jet is responsible for the dispersion of Rossby waves by the cyclones and the development of an anticyclonic anomaly in the upper layer. This anticyclone forms a PV dipole with the upper-layer cyclone that nonlinearly advects the lower-layer cyclone across the jet. In addition, the background deformation is shown to modulate the cross-jet advection. Cyclones evolving in a deformation-dominated environment (south of troughs) are strongly stretched while those evolving in a rotation-dominated environment (south of ridges) remain quasi isotropic. It is shown that the more stretched cyclones trigger a more efficient dispersion of energy, create a stronger upper-layer anticyclone, and move perpendicularly to the jet faster than the less stretched ones. Both the intensity and location of the upper-layer anticyclone explain the distinct cross-jet speeds. A statistical study consisting in initializing cyclones at different locations south of the jet core confirms that the cross-jet motion is faster for the more meridionally elongated cyclones evolving in areas of strongest barotropic PV gradient.

scholarly journals Low-frequency variability of the Kuroshio Extension

2009 ◽  
Vol 16 (6) ◽  
pp. 665-675 ◽  
Author(s):  
S. Pierini ◽  
H. A. Dijkstra
Keyword(s):  
Nonlinear Dynamics ◽  
Large Scale ◽  
Rossby Waves ◽  
Kuroshio Extension ◽  
Baroclinic Instability ◽  
Low Frequency ◽  
Wave Dynamics ◽  
Low Frequency Variability ◽  
Low Dimensional ◽  
The Kuroshio

Abstract. In this paper, we provide a review of recent results targeted at the understanding of the low-frequency variability of the Kuroshio Extension. We provide the background and main arguments of two views which have recently been proposed to explain this variability. In the first view, wind-induced Rossby waves and the effects of mesocale eddies are crucial. The second view is based on low-dimensional equivalent-barotropic large-scale nonlinear dynamics, with neither Rossby wave dynamics nor baroclinic instability being important. Results from models supporting each view are discussed and confronted with results from available observations.

Baroclinic instability of large-amplitude geostrophic flows

1993 ◽  
Vol 251 ◽  
pp. 501-514 ◽  
Author(s):  
E. S. Benilov
Keyword(s):  
Large Amplitude ◽  
Large Scale ◽  
Hamiltonian Structure ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Vertical Shear ◽  
Governing Equations ◽  
Zonal Flows ◽  
Wave Disturbances ◽  
Geostrophic Flows

This paper examines the large-scale dynamics of a layer of stratified fluid on the β-plane. A three-dimensional asymptotic system is derived which governs geostrophic flows with large displacement of isopycnal surfaces. This is then reduced to a two-dimensional set of equations which describe the interaction of a baroclinic ‘quasi-mode’ with arbitrary vertical profile and barotrophic motion. The baroclinic instability of large-amplitude zonal flows with vertical shear is studied within the framework of these equations. In the case where the displacement of isopycnal surfaces is small, the results obtained should overlap with the ‘traditional’ baroclinic instability of quasi-geostrophic (small-amplitude) flows. In order to compare the two types of instability, the quasi-geostrophic boundary-value problem is solved asymptotically for the case of long-wave disturbances and weak β-effect (the latter limit of quasi-geostrophic theory has not been considered previously). The instability that is found is linked to the Hamiltonian structure of the governing equations. The equations derived are generalized for the case of more than one baroclinic quasi-mode.

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