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 Upgradient and Downgradient Potential Vorticity Fluxes Produced by Forced Rossby Waves. Part II: Parameter Sensitivity and Physical Interpretation

2018 ◽  
Vol 48 (5) ◽  
pp. 1211-1230 ◽  
Author(s):  
Genta Mizuta
Keyword(s):  
Potential Vorticity ◽  
Rossby Waves ◽  
Lower Layer ◽  
External Forcing ◽  
Direct Effects ◽  
Horizontal Scale ◽  
Wave Interactions ◽  
Weak Stratification ◽  
Quasigeostrophic Model ◽  
Basic Features

AbstractWe examine the potential vorticity (PV) flux produced by forced Rossby waves in a two-layer quasigeostrophic model, using a perturbation analysis. Rossby waves are excited by external forcing applied to the upper layer. The southward PV flux is produced in the lower layer by the higher-order Rossby waves that are excited by nonlinear wave–wave interactions, whereas the northward PV flux is produced in the upper layer. The direction of the PV flux is consistent with that obtained by an eddy-resolving model of the wind-driven circulation in previous studies. The southward PV flux is produced in a wide parameter range comparable to the eddy-resolving model. The basic features of the PV flux remain unchanged even in the limit of weak stratification. In this limit, stratification has nearly no effect on the flow, except that it isolates the lower layer from the direct effects of external forcing. The mechanism of the southward PV flux is explained using basic features of the barotropic Rossby waves and does not depend on details of the model. Furthermore, the resonant triad interaction of Rossby waves does not affect the PV flux. Stratification weakens or strengthens the PV flux depending on the horizontal scale of the external forcing.

Finite-Amplitude Equilibration of Baroclinic Waves on a Jet

2010 ◽  
Vol 67 (2) ◽  
pp. 434-451 ◽  
Author(s):  
Sukyoung Lee
Keyword(s):  
Wave Breaking ◽  
Lower Layer ◽  
Finite Amplitude ◽  
Primary Role ◽  
Ekman Pumping ◽  
Amplitude Wave ◽  
Wave Source ◽  
Model Calculations ◽  
Baroclinic Waves ◽  
Pv Gradient

Abstract A two-layer quasigeostrophic model is used to study the equilibration of baroclinic waves. In this model, if the background flow is relaxed toward a jetlike profile, a finite-amplitude baroclinic wave solution can be realized in both supercritical and subcritical regions of the model’s parameter space. Analyses of the model equations and numerical model calculations indicate that the finite-amplitude wave equilibration hinges on the breaking of Rossby waves before they reach their critical latitude. This “jetward” wave breaking results in an increase in the upper-layer wave generation and a reduction in the vertical phase tilt. This change in the phase tilt has a substantial impact on the Ekman pumping, as it weakens the damping on the lower-layer wave for some parameter settings and enables the Ekman pumping to serve as a source of wave growth at other settings. Together, these processes can account for the O(1)-amplitude wave equilibration. From a potential vorticity (PV) perspective, the wave breaking reduces the meridional scale of the upper-layer eddy PV flux, which destabilizes the mean flow. This is followed by a strengthening of the lower-layer eddy PV flux, which weakens the lower-layer PV gradient and constrains the growth of the lower-layer eddy PV. The same jetward wave breaking focuses the upper-layer PV flux toward the jet center where the upper-layer PV gradient is greatest. This results in an intensification of the upper-layer eddy PV relative to lower-layer eddy PV. Because of this large ratio, the upper-layer eddy PV plays the primary role in inducing the upper- and lower-layer eddy streamfunction fields, decreasing the vertical phase tilt. As a result, the Ekman pumping on the eddies is weakened, and for some parameter settings the Ekman pumping can even act as a wave source, contributing toward O(1)-amplitude wave equilibration. By reducing the horizontal shear of the zonal wind, the same wave breaking process weakens the barotropic decay, which also contributes to the wave amplification.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

2009 ◽  
Vol 66 (6) ◽  
pp. 1735-1748 ◽  
Author(s):  
W. T. M. Verkley
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Rossby Waves ◽  
Coriolis Parameter ◽  
Beta Plane ◽  
Propagating Waves ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity ◽  
The One

Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

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 Role of Surface-Layer Coherent Eddies in Potential Vorticity Transport in Quasigeostrophic Turbulence Driven by Eastward Shear

Fluids ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 2
Author(s):  
Wenda Zhang ◽  
Christopher L. P. Wolfe ◽  
Ryan Abernathey
Keyword(s):  
Surface Layer ◽  
Potential Vorticity ◽  
Model Driven ◽  
Wide Range ◽  
Stirring Effect ◽  
Geophysical Turbulence ◽  
Quasigeostrophic Model ◽  
Vorticity Transport ◽  
Pv Gradient

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10–20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient PV transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 15% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. These results clarify the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence.

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 Finite-Amplitude Wave Activity and Diffusive Flux of Potential Vorticity in Eddy–Mean Flow Interaction

2010 ◽  
Vol 67 (9) ◽  
pp. 2701-2716 ◽  
Author(s):  
Noboru Nakamura ◽  
Da Zhu
Keyword(s):  
Potential Vorticity ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Diffusive Flux ◽  
Mean Flow ◽  
Amplitude Wave ◽  
Flow Modification ◽  
Flow Interaction ◽  
Beta Plane ◽  
Finite Amplitude Wave Activity

Abstract An exact diagnostic formalism for finite-amplitude eddy–mean flow interaction is developed for barotropic and quasigeostrophic baroclinic flows on the beta plane. Based on the advection–diffusion–reaction equation for potential vorticity (PV), the formalism quantifies both advective and diffusive contributions to the mean flow modification by eddies, of which the latter is the focus of the present article. The present theory adopts a hybrid Eulerian–Lagrangian-mean description of the flow and defines finite-amplitude wave activity in terms of the areal displacement of PV contours from zonal symmetry. Unlike previous formalisms, wave activity is readily calculable from data and the local Eliassen–Palm relation does not involve cubic or higher-order terms in eddy amplitude. This leads to a natural finite-amplitude extension to the local nonacceleration theorem, as well as the global stability theorems, in the inviscid and unforced limit. The formalism incorporates mixing with effective diffusivity of PV, and the diffusive flux of PV is shown to be a sink of wave activity. The relationship between the advective and diffusive fluxes of PV and its implications for parameterization are discussed in the context of wave activity budget. If all momentum associated with wave activity were returned to the zonal-mean flow, a balanced eddy-free flow would ensue. It is shown that this hypothetical flow uREF is unaffected by the advective PV flux and is driven solely by the diffusive PV flux and forcing. For this reason, uREF, rather than the zonal-mean flow, is proposed as a diagnostic for the diffusive mean-flow modification. The formalism is applied to a freely decaying beta-plane turbulence to evaluate the contribution of the diffusive PV flux to the jet formation.

scholarly journals On the Northward Motion of Midlatitude Cyclones in a Barotropic Meandering Jet

2012 ◽  
Vol 69 (6) ◽  
pp. 1793-1810 ◽  
Author(s):  
Ludivine Oruba ◽  
Guillaume Lapeyre ◽  
Gwendal Rivière
Keyword(s):  
Statistical Study ◽  
Relative Vorticity ◽  
Wave Radiation ◽  
Zonal Flows ◽  
Vortex Dipole ◽  
Beta Plane ◽  
Cyclonic Vortex ◽  
Quasigeostrophic Model ◽  
Spatially Varying ◽  
Midlatitude Cyclones

Abstract The combined effects of the deformation (horizontal stretching and shearing) and nonlinearities on the beta drift of midlatitude cyclones are studied using a barotropic quasigeostrophic model on the beta plane. It is found that, without any background flow, a cyclonic vortex moves more rapidly northward when it is initially strongly stretched along a mostly north–south direction. This meridional stretching is more efficient at forming an anticyclone to the east of the cyclone through Rossby wave radiation. The cyclone–anticyclone couple then forms a nonlinear vortex dipole that propagates mostly northward. The case of a cyclone embedded in uniformly sheared zonal flows is then studied. A cyclone evolving in an anticyclonic shear is stretched more strongly, develops a stronger anticyclone, and moves faster northward than a cyclone embedded in a cyclonic shear, which remains almost isotropic. Similar results are found in the general case of uniformly sheared nonzonal flows. The evolution of cyclones is also investigated in the case of a more realistic meandering jet whose relative vorticity gradient creates an effective beta and whose deformation field is spatially varying. A statistical study reveals a strong correlation among the cyclone’s stretching, the anticyclone strength, and the velocity toward the jet center. These different observations agree with the more idealized cases. Finally, these results provide a rationale for the existence of preferential zones for the jet-crossing phase: that is, the phase when a cyclone crosses a jet from its anticyclonic to its cyclonic side.

Vortex Dipole Formation by Baroclinic Instability of Boundary Currents

2007 ◽  
Vol 37 (6) ◽  
pp. 1661-1677 ◽  
Author(s):  
L. Chérubin ◽  
X. Carton ◽  
D. G. Dritschel
Keyword(s):  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Point Vortex ◽  
Wave Dispersion ◽  
Finite Amplitude ◽  
Layer Potential ◽  
Weakly Nonlinear ◽  
In Situ Data ◽  
Vortex Dipole ◽  
Quasigeostrophic Model

Abstract In situ data of the Mediterranean Water undercurrents and eddies south of Portugal indicate that the undercurrents have a tubelike structure in potential vorticity and that dipole formation can occur when the lower undercurrent extends seaward below an offshore upper countercurrent. A two-layer quasigeostrophic model is used to determine the dynamical conditions under which dipole formation is possible. With piecewise-constant potential vorticity, the flow exhibits two linear modes of instability comparable to those found in the Phillips model with topography. Weakly nonlinear analysis and fully nonlinear simulations of the flow evolution agree on the regimes of either finite-amplitude perturbation saturation, corresponding to filamentation, or amplification, corresponding to vortex or dipole formation. This latter regime is more specifically studied: vortex dipole formation and ejection from the coast is obtained for long waves, with opposite-signed but similar amplitude layer potential vorticities. A simple point vortex model reproduces this phenomenon under the same conditions. It is then shown that dipole formation occurs for minimal wave dispersion, and hence for weak horizontal velocity shears. As observed at sea, dipoles are formed when the lower potential vorticity core extends seaward below a countercurrent.

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