scholarly journals Linear baroclinic instability in the Martian atmosphere: Primitive equation calculations

1999 ◽  
Vol 51 (3) ◽  
pp. 225-232 ◽  
Author(s):  
H. L. Tanaka ◽  
Mayumi Arai
Keyword(s):  
Baroclinic Instability ◽  
Martian Atmosphere ◽  
Primitive Equation

Seasonal Variability of Mesoscale Instabilities in the Azores Current System

2020 ◽  
Author(s):  
João Bettencourt ◽  
Carlos Guedes Soares
Keyword(s):  
Kinetic Energy ◽  
Reynolds Stress ◽  
North Atlantic ◽  
Current System ◽  
Baroclinic Instability ◽  
Primitive Equation ◽  
The Mean ◽  
Eastern North Atlantic ◽  
Jet Axis ◽  
Mean Kinetic Energy

<p>The Azores Current-Front system coincides with the northern limit of the subtropical gyre in  the Eastern North Atlantic. The mean zonal jet is positioned south of the Azores archipelago  and extends from west of the mid-atlantic ridge to the Gulf of Cadiz, where it partially  turns south. North of the main jet, a sub-surface counter-current is found, flowing westwards. The associated thermal front separates the warm subtropical waters from the colder subpolar waters. The instantaneous flow in the Azores Current/Front system is characterized by the presence of meandering currents with length scales of 200 km that regularly shed anticyclonic warm water and cyclonic cold water eddies to the north and south of the mean jet axis, respectively, due to vortex stretching and the planetary beta effect. The time scale of eddy shedding is 100-200 days. On the meandering arms of the current, downwelling <br>and upwelling cells are found and sharp thermal gradients are formed and a residual poleward heat transport is observed. The instability cycle that originates the mesoscale meanders and the eddies is well-known from quasi-geostrophic and primitive equation models initialized from a basic baroclinic state: a first phase of baroclinic instability feeds on available potential energy to raise eddy kinetic energy levels, that, in a second phase feed the mean kinetic energy by Reynolds stress convergence. The cycle repeats itself as long as the APE reservoir is filled at the end of each cycle.</p><p>However, seasonal variability of the zonal jet dynamics has not been addressed before and it can provide valuable insights in to the variations of the Eastern North Atlantic between the subtropical and subpolar gyres. We use a primitive equation regional ocean model of the Eastern Central North Atlantic with realistic climatological wind and thermal forcing to study the yearly cycle of meandering, eddy shedding and restoration of the mean jet in the Azores/Current system. We observe an semi-annual cycle in the jet's kinetic energy with maxima in Summer/Winter and minima in early Spring/Autumn. Potential energy conversion by baroclinic instability occurs throughout the year but is predominant in the first half of the year. The mean kinetic energy draws from the turbulent kinetic energy through Reynolds stress convergence in periods of 50 - 100 days, that are followed by short barotropic instability periods. During Winter, Reynolds stress convergence, and thus mean jet reinforcement from the mesoscale eddy field, occurs along the jet meridional extent, in the top 500 m of the water column, but from Spring to Autumn it is observed only in the southern flank of the mean jet axis.</p>

scholarly journals Is a Real Cyclogenesis Case Explained by Generalized Linear Baroclinic Instability?

2007 ◽  
Vol 64 (12) ◽  
pp. 4287-4308 ◽  
Author(s):  
L. Descamps ◽  
D. Ricard ◽  
A. Joly ◽  
P. Arbogast
Keyword(s):  
Singular Vector ◽  
Baroclinic Instability ◽  
Jet Flow ◽  
Theoretical Framework ◽  
The Other ◽  
Relevant Model ◽  
Primitive Equation ◽  
Intense Storm ◽  
Model Equations ◽  
Actual Realization

Abstract Midlatitude cyclogenesis is currently often explained as resulting from the baroclinic instability of a jet flow. The present formulation of the theory, essentially resulting from the deep revision performed by Farrell, associates incipient cyclones with amplifying singular vectors of a linear propagator operator obtained by linearizing the relevant model equations (balanced or not) about a trajectory representing the jet flow alone. A major difficulty for transposing the theoretical framework to a real case, and then opening the way to quantitative verifications of the theory, is this separation of an actual realization of cyclogenesis into the cyclone as a perturbation on one side and its environment on the other. A methodology to obtain such a separation in a reasonably objective and dynamically consistent way is presented. It enables obtaining two diabatic primitive equation solutions about the 26 December 1999 intense storm, one that has the event and the other that has most of the characteristics of the exceptional baroclinic environment of that case, except the storm itself. It is then possible to employ the theoretical framework without further approximation and to compare the predicted unstable modes with the storm representing itself as a perturbation. Two aspects of the theory are especially studied. One is a comparison of the properties of the real and predicted systems, focusing on their structures. The other deals with the idea that precursor structures, although very different from the theoretical modes, trigger the cyclogenesis by exciting these modes. It appears that the classical predictions (scales, etc.) of such a theory are, for most of them, far away from the observed properties. It is clear that the structure of a singular vector has little to share with that of a real cyclone. Yet, a weaker, slower storm does occur as a result of applying the theory to the stormless trajectory.

Equilibration of Baroclinic Turbulence in Primitive Equations and Quasigeostrophic Models

2009 ◽  
Vol 66 (4) ◽  
pp. 837-863 ◽  
Author(s):  
Pablo Zurita-Gotor ◽  
Geoffrey K. Vallis
Keyword(s):  
Baroclinic Instability ◽  
Quantitative Agreement ◽  
Equation Model ◽  
Turbulence Theory ◽  
Mean Flow ◽  
Primitive Equation ◽  
Primitive Equation Model ◽  
Barotropic Flow ◽  
Quasigeostrophic Model ◽  
Parameter Ranges

Abstract This paper investigates the equilibration of baroclinic turbulence in an idealized, primitive equation, two-level model, focusing on the relation with the phenomenology of quasigeostrophic turbulence theory. Simulations with a comparable two-layer quasigeostrophic model are presented for comparison, with the deformation radius in the quasigeostrophic model being set using the stratification from the primitive equation model. Over a fairly broad parameter range, the primitive equation and quasigeostrophic results are in qualitative and, to some degree, quantitative agreement and are consistent with the phenomenology of geostrophic turbulence. The scale, amplitude, and baroclinicity of the eddies and the degree of baroclinic instability of the mean flow all vary fairly smoothly with the imposed parameters; both models are able, in some parameter ranges, to produce supercritical flows. The criticality in the primitive equation model, which does not have any convective parameterization scheme, is fairly sensitive to the external parameters, most notably the planet size (i.e., the f /β ratio), the forcing time scale, and the factors influencing the stratification. In some parameter settings of the models, although not those that are most realistic for the earth’s atmosphere, it is possible to produce eddies that are considerably larger than the deformation scales and an inverse cascade in the barotropic flow with a −5/3 spectrum. The vertical flux of heat is found to be related to the isentropic slope.

Why Anticyclones Can Split

2003 ◽  
Vol 33 (8) ◽  
pp. 1579-1591 ◽  
Author(s):  
S. S. Drijfhout
Keyword(s):  
Deep Layer ◽  
Baroclinic Instability ◽  
Equation Model ◽  
Vertical Transport ◽  
Phase Lag ◽  
Primitive Equation ◽  
Baroclinic Energy Conversion ◽  
Break Up ◽  
Baroclinic Vortices ◽  
Surrounding Fluid

Abstract The question of whether anticyclones can split and break up is readdressed using a numerical, multilayer, primitive equation model. Applying the conservation of integrated angular momentum (IAM) to barotropic and baroclinic vortices, it has been argued that anticyclones can never split, no matter what their structure is. When an anticyclone splits, the IAM has to increase as the newly formed eddies are pushed away from their original center. Conservation of IAM prohibits such an increase. Several numerical simulations, however, have shown anticyclonic splitting. In a multilayer model, a vertical transport of IAM is possible. For counterrotating eddies (an anticyclone on top of a cyclone) it is easy to see that a vertical exchange of IAM allows the eddy to break up. For a compensated or weakly corotating eddy, breakup is only possible when, in addition to a vertical transport of IAM, in the deep layer(s) IAM is exchanged between the core of the vortex and the surrounding fluid. In the presence of a tilting interface, the pressure gradient associated with the sea surface height (SSH) anomaly, in particular its non-equivalent-barotropic part, drives the required exchanges. The non-equivalent-barotropic SSH anomaly is associated with the vertical phase lag of the most unstable eigenmode (m = 2), which develops when this mode gains energy by baroclinic energy conversion. The previous conclusion that anticyclones cannot split on their own should be revised to the following: anticyclones cannot split by barotropic processes alone—baroclinic instability is a necessary ingredient for splitting to occur.

Baroclinic Turbulence in the Ocean: Analysis with Primitive Equation and Quasigeostrophic Simulations

2011 ◽  
Vol 41 (9) ◽  
pp. 1605-1623 ◽  
Author(s):  
Antoine Venaille ◽  
Geoffrey K. Vallis ◽  
K. Shafer Smith
Keyword(s):  
Southern Ocean ◽  
Energy Levels ◽  
Baroclinic Instability ◽  
Primary Source ◽  
Equation Model ◽  
Ocean Modeling ◽  
Length Scale ◽  
Primitive Equation ◽  
Eddy Field ◽  
Quasigeostrophic Model

Abstract This paper examines the factors determining the distribution, length scale, magnitude, and structure of mesoscale oceanic eddies in an eddy-resolving primitive equation simulation of the Southern Ocean [Modeling Eddies in the Southern Ocean (MESO)]. In particular, the authors investigate the hypothesis that the primary source of mesoscale eddies is baroclinic instability acting locally on the mean state. Using local mean vertical profiles of shear and stratification from an eddying primitive equation simulation, the forced–dissipated quasigeostrophic equations are integrated in a doubly periodic domain at various locations. The scales, energy levels, and structure of the eddies found in the MESO simulation are compared to those predicted by linear stability analysis, as well as to the eddying structure of the quasigeostrophic simulations. This allows the authors to quantitatively estimate the role of local nonlinear effects and cascade phenomena in the generation of the eddy field. There is a modest transfer of energy (an “inverse cascade”) to larger scales in the horizontal, with the length scale of the resulting eddies typically comparable to or somewhat larger than the wavelength of the most unstable mode. The eddies are, however, manifestly nonlinear, and in many locations the turbulence is fairly well developed. Coherent structures also ubiquitously emerge during the nonlinear evolution of the eddy field. There is a near-universal tendency toward the production of grave vertical scales, with the barotropic and first baroclinic modes dominating almost everywhere, but there is a degree of surface intensification that is not captured by these modes. Although the results from the local quasigeostrophic model compare well with those of the primitive equation model in many locations, some profiles do not equilibrate in the quasigeostrophic model. In many cases, bottom friction plays an important quantitative role in determining the final scale and magnitude of eddies in the quasigeostrophic simulations.

scholarly journals Local Dynamics of Baroclinic Waves in the Martian Atmosphere

2013 ◽  
Vol 70 (11) ◽  
pp. 3415-3447 ◽  
Author(s):  
Michael J. Kavulich ◽  
Istvan Szunyogh ◽  
Gyorgyi Gyarmati ◽  
R. John Wilson
Keyword(s):  
General Circulation ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Circulation Model ◽  
Regular Structure ◽  
Martian Atmosphere ◽  
Geophysical Fluid Dynamics Laboratory ◽  
Global Features ◽  
Baroclinic Waves ◽  
Zonal Wavenumber

Abstract The paper investigates the processes that drive the spatiotemporal evolution of baroclinic transient waves in the Martian atmosphere by a simulation experiment with the Geophysical Fluid Dynamics Laboratory (GFDL) Mars general circulation model (GCM). The main diagnostic tool of the study is the (local) eddy kinetic energy equation. Results are shown for a prewinter season of the Northern Hemisphere, in which a deep baroclinic wave of zonal wavenumber 2 circles the planet at an eastward phase speed of about 70° Sol−1 (Sol is a Martian day). The regular structure of the wave gives the impression that the classical models of baroclinic instability, which describe the underlying process by a temporally unstable global wave (e.g., Eady model and Charney model), may have a direct relevance for the description of the Martian baroclinic waves. The results of the diagnostic calculations show, however, that while the Martian waves remain zonally global features at all times, there are large spatiotemporal changes in their amplitude. The most intense episodes of baroclinic energy conversion, which take place in the two great plain regions (Acidalia Planitia and Utopia Planitia), are strongly localized in both space and time. In addition, similar to the situation for terrestrial baroclinic waves, geopotential flux convergence plays an important role in the dynamics of the downstream-propagating unstable waves.

scholarly journals Dynamics of Midlatitude Tropopause Height in an Idealized Model

2011 ◽  
Vol 68 (4) ◽  
pp. 823-838 ◽  
Author(s):  
Pablo Zurita-Gotor ◽  
Geoffrey K. Vallis
Keyword(s):  
Baroclinic Instability ◽  
Equation Model ◽  
Tropopause Height ◽  
Mean Flow ◽  
Flow Properties ◽  
Primitive Equation ◽  
Conservation Of Energy ◽  
Primitive Equation Model ◽  
Eddy Transport ◽  
The Mean

Abstract This paper investigates the factors that determine the equilibrium state, and in particular the height and structure of the tropopause, in an idealized primitive equation model forced by Newtonian cooling in which the eddies can determine their own depth. Previous work has suggested that the midlatitude tropopause height may be understood as the intersection between a radiative and a dynamical constraint. The dynamical constraint relates to the lateral transfer of energy, which in midlatitudes is largely effected by baroclinic eddies, and its representation in terms of mean-flow properties. Various theories have been proposed and investigated for the representation of the eddy transport in terms of the mean flow, including a number of diffusive closures and the notion that the flow evolves to a state marginally supercritical to baroclinic instability. The radiative constraint expresses conservation of energy and so must be satisfied, although it need not necessarily be useful in providing a tight constraint on tropopause height. This paper explores whether and how the marginal criticality and radiative constraints work together to produce an equilibrated flow and a tropopause that is internal to the fluid. The paper investigates whether these two constraints are consistent with simulated variations in the tropopause height and in the mean state when the external parameters of an idealized primitive equation model are changed. It is found that when the vertical redistribution of heat is important, the radiative constraint tightly constrains the tropopause height and prevents an adjustment to marginal criticality. In contrast, when the stratification adjustment is small, the radiative constraint is only loosely satisfied and there is a tendency for the flow to adjust to marginal criticality. In those cases an alternative dynamical constraint would be needed in order to close the problem and determine the eddy transport and tropopause height in terms of forcing and mean flow.

scholarly journals Equatorial Superrotation and Barotropic Instability: Static Stability Variants

2006 ◽  
Vol 63 (5) ◽  
pp. 1548-1557 ◽  
Author(s):  
G. P. Williams
Keyword(s):  
Atmospheric Circulation ◽  
Baroclinic Instability ◽  
Static Stability ◽  
Equation Model ◽  
Primary Process ◽  
Barotropic Instability ◽  
Newtonian Heating ◽  
Low Latitude ◽  
Primitive Equation ◽  
Model Subject

Abstract Altering the tropospheric static stability changes the nature of the equatorial superrotation associated with unstable, low-latitude, westerly jets, according to calculations with a dry, global, multilevel, spectral, primitive equation model subject to a simple Newtonian heating function. For a low static stability, the superrotation fluxes with the simplest structure occur when the stratospheric extent and horizontal diffusion are minimal. Barotropic instability occurs on the jet's equatorward flank and baroclinic instability occurs on the jet's poleward flank. Systems with a high static stability inhibit the baroclinic instability and thereby reveal more clearly that the barotropic instability is the primary process driving the equatorial superrotation. Such systems produce a flatter equatorial jet and also take much longer to equilibrate than the standard atmospheric circulation.

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