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.

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>

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.

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.

scholarly journals Nonlinear evolution of a baroclinic wave and imbalanced dissipation

2014 ◽  
Vol 756 ◽  
pp. 965-1006 ◽  
Author(s):  
Balasubramanya T. Nadiga
Keyword(s):  
Large Scale ◽  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Base Flow ◽  
Vertical Shear ◽  
Baroclinic Wave ◽  
Set Up ◽  
Secondary Instabilities

AbstractWe consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere: a regime characterized by small large-scale Rossby and Froude numbers, a small vertical to horizontal aspect ratio and no bounding horizontal surfaces. Using high-resolution simulations of the non-hydrostatic Boussinesq equations and companion integrations of the balanced quasi-geostrophic (QG) equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. That is, analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales whereas the bulk of the energy is confined to large balanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These two processes acting together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall slowly when frontogenesis slows down; eventually balanced and imbalanced modes decouple. A measurement of the dissipation of balanced energy by imbalanced processes reveals that it scales exponentially with Rossby number of the base flow. We expect that this scaling will hold more generally than for the specific set-up we consider given the fundamental nature of the dynamics involved. In other results, (a) a break is seen in the total energy (TE) spectrum at small scales: while a steep $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}k^{-3}$ geostrophic scaling (where $k$ is the three-dimensional wavenumber) is seen at intermediate scales, the smaller scales display a shallower $k^{-5/3}$ scaling, reminiscent of the atmospheric spectra of Nastrom & Gage and (b) at the higher of the Rossby numbers considered a minimum is seen in the vertical shear spectrum, reminiscent of similar spectra obtained using in situ measurements.

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.

scholarly journals Stability Analysis of the Labrador Current

2014 ◽  
Vol 44 (2) ◽  
pp. 445-463 ◽  
Author(s):  
Sören Thomsen ◽  
Carsten Eden ◽  
Lars Czeschel
Keyword(s):  
Stability Analysis ◽  
Growth Rates ◽  
Baroclinic Instability ◽  
Cross Flow ◽  
Vertical Shear ◽  
Maximal Growth ◽  
Phase Velocities ◽  
Labrador Current ◽  
Lateral Mixing ◽  
Weak Stratification

Abstract Mooring observations and model simulations point to an instability of the Labrador Current (LC) during winter, with enhanced eddy kinetic energy (EKE) at periods between 2 and 5 days and much less EKE during other seasons. Linear stability analysis using vertical shear and stratification from the model reveals three dominant modes of instability in the LC: 1) a balanced interior mode with along-flow wavelengths of about 30–45 km, phase velocities of 0.3 m s−1, maximal growth rates of 1 day−1, and surface-intensified but deep-reaching amplitudes; 2) a balanced shallow mode with along-flow wavelengths of about 0.3–1.5 km, phase velocities of 0.55 m s−1, about 3 times larger growth rates, but amplitudes confined to the mixed layer (ML); and 3) an unbalanced symmetric mode with the largest growth rates, vanishing phase speeds, and along-flow structure, and very small cross-flow wavelengths, also confined to the ML. Both balanced modes are akin to baroclinic instability but operate at moderate-to-small Richardson numbers Ri with much larger growth rates as for the quasigeostrophic limit of Ri ≫ 1. The interior mode is found to be responsible for the instability of the LC during winter. Weak stratification and enhanced vertical shear due to local buoyancy loss and the advection of convective water masses from the interior result in small Ri within the LC and up to 3 times larger growth rates of the interior mode in March compared to summer and fall conditions. Both the shallow and the symmetric modes are not resolved by the model, but it is suggested that they might also play an important role for the instability in the LC and for lateral mixing.

Experiments with baroclinic vortex pairs in a rotating fluid

1986 ◽  
Vol 173 ◽  
pp. 501-518 ◽  
Author(s):  
R. W. Griffiths ◽  
E. J. Hopfinger
Keyword(s):  
Velocity Field ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Point Vortices ◽  
Density Stratification ◽  
Rotating Fluid ◽  
Vortex Pairs ◽  
Layer Density

When vortices are generated in one layer of a rotating, two-layer density stratification, the velocity field of each vortex is strongly baroclinic within a distance of order one Rossby radius from its centre. In this system there are two classes of vortex pairs: those pairs (consisting of vortices of opposite signs) for which the vortices are in the same layer, and those for which the vortices are in opposite layers. We pay particular attention to a laboratory demonstration of the properties of the latter class. These vortex pairs have the ability to transport density (or heat) in the horizontal, and provide a means for describing the release of potential energy by baroclinic instability. We also observe that interactions of real vortices and real vortex pairs differ from those computed for point vortices.

scholarly journals Instabilities of continuously stratified zonal equatorial jets in a periodic channel model

2002 ◽  
Vol 20 (5) ◽  
pp. 729-740 ◽  
Author(s):  
S. Masina
Keyword(s):  
Channel Model ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Maximum Velocity ◽  
Equatorial Region ◽  
Eastern Pacific ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Vertical Scale ◽  
Surface Jet

Abstract. Several numerical experiments are performed in a nonlinear, multi-level periodic channel model centered on the equator with different zonally uniform background flows which resemble the South Equatorial Current (SEC). Analysis of the simulations focuses on identifying stability criteria for a continuously stratified fluid near the equator. A 90 m deep frontal layer is required to destabilize a zonally uniform, 10° wide, westward surface jet that is symmetric about the equator and has a maximum velocity of 100 cm/s. In this case, the phase velocity of the excited unstable waves is very similar to the phase speed of the Tropical Instability Waves (TIWs) observed in the eastern Pacific Ocean. The vertical scale of the baroclinic waves corresponds to the frontal layer depth and their phase speed increases as the vertical shear of the jet is doubled. When the westward surface parabolic jet is made asymmetric about the equator, in order to simulate more realistically the structure of the SEC in the eastern Pacific, two kinds of instability are generated. The oscillations that grow north of the equator have a baroclinic nature, while those generated on and very close to the equator have a barotropic nature.  This study shows that the potential for baroclinic instability in the equatorial region can be as large as at mid-latitudes, if the tendency of isotherms to have a smaller slope for a given zonal velocity, when the Coriolis parameter vanishes, is compensated for by the wind effect.Key words. Oceanography: general (equatorial oceanography; numerical modeling) – Oceanography: physics (fronts and jets)

scholarly journals Reintensification and Eyewall Formation in Strong Shear: A Case Study of Typhoon Noul (2015)

2018 ◽  
Vol 146 (9) ◽  
pp. 2799-2817 ◽  
Author(s):  
Udai Shimada ◽  
Takeshi Horinouchi
Keyword(s):  
Doppler Radar ◽  
Vertical Wind Shear ◽  
Vertical Shear ◽  
Tangential Wind ◽  
Strong Shear ◽  
Vertically Aligned ◽  
Mean Structure ◽  
Convection Dominated ◽  
Left Quadrant

Abstract Strong vertical wind shear produces asymmetries in the eyewall structure of a tropical cyclone (TC) and is generally a hostile environment for TC intensification. Typhoon Noul (2015), however, reintensified and formed a closed eyewall despite 200–850-hPa vertical shear in excess of 11 m s−1. Noul’s reintensification and eyewall formation in strong shear were examined by using Doppler radar and surface observations. The evolution of the azimuthal-mean structure showed that the tangential wind at 2-km altitude increased from 30 to 45 m s−1 in only 5 h. During the first half of the reintensification, the azimuthal-mean inflow penetrated into the ~40-km radius, well inside the radius of maximum wind (RMW), at least below 4-km altitude, and reflectivity inside the RMW increased. As for the asymmetric evolution, vigorous convection, dominated by an azimuthal wavenumber-1 asymmetry, occurred in the downshear-left quadrant when shear started to increase and then moved upshear. A mesovortex formed inside the convective asymmetry on the upshear side. The direction of vortex tilt between the 1- and 5-km altitudes rotated cyclonically from the downshear-left to the upshear-right quadrant as the vortex was vertically aligned. In conjunction with the alignment, the amplitude of the wavenumber-1 convective asymmetry decreased and a closed eyewall formed. These features are consistent with the theory that a vortex can be vertically aligned through upshear precession. The analysis results suggest that the vortex tilt, vigorous convection, and subsequent intensification were triggered by the increase in shear in a convectively favorable environment.

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