scholarly journals The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

2005 ◽  
Vol 131 (608) ◽  
pp. 1393-1424 ◽  
Author(s):  
J. Methven ◽  
E. Heifetz ◽  
B. J. Hoskins ◽  
C. H. Bishop
Keyword(s):  
Rossby Wave ◽  
Baroclinic Instability ◽  
Primitive Equation

scholarly journals The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

2004 ◽  
Vol 130 (596) ◽  
pp. 233-258 ◽  
Author(s):  
E. Heifetz ◽  
J. Methven ◽  
B. J. Hoskins ◽  
C. H. Bishop
Keyword(s):  
Rossby Wave ◽  
Baroclinic Instability

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.

Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers

2008 ◽  
Vol 65 (3) ◽  
pp. 855-874 ◽  
Author(s):  
D. G. Dritschel ◽  
M. E. McIntyre
Keyword(s):  
Rossby Wave ◽  
Positive Feedback ◽  
Baroclinic Instability ◽  
Turbulence Theory ◽  
Core Size ◽  
Radiation Stress ◽  
New Paradigm ◽  
Nonlinear Disturbances ◽  
Transport Barriers ◽  
Eddy Transport

Abstract A review is given that focuses on why the sideways mixing of potential vorticity (PV) across its background gradient tends to be inhomogeneous, arguably a reason why persistent jets are commonplace in planetary atmospheres and oceans, and why such jets tend to sharpen themselves when disturbed. PV mixing often produces a sideways layering or banding of the PV distribution and therefore a corresponding number of jets, as dictated by PV inversion. There is a positive feedback in which mixing weakens the “Rossby wave elasticity” associated with the sideways PV gradients, facilitating further mixing. A partial analogy is drawn with the Phillips effect, the spontaneous layering of a stably stratified fluid, in which vertically homogeneous stirring produces vertically inhomogeneous mixing of the background buoyancy gradient. The Phillips effect has been extensively studied and has been clearly demonstrated in laboratory experiments. However, the “eddy-transport barriers” and sharp jets characteristic of extreme PV inhomogeneity, associated with strong PV mixing and strong sideways layering into Jupiter-like “PV staircases,” with sharp PV contrasts Δqbarrier, say, involve two additional factors besides the Rossby wave elasticity concentrated at the barriers. The first is shear straining by the colocated eastward jets. PV inversion implies that the jets are an essential, not an incidental, part of the barrier structure. The shear straining increases the barriers’ resilience and amplifies the positive feedback. The second is the role of the accompanying radiation-stress field, which mediates the angular-momentum changes associated with PV mixing and points to a new paradigm for Jupiter, in which the radiation stress is excited not by baroclinic instability but by internal convective eddies nudging the Taylor–Proudman roots of the jets. Some examples of the shear-straining effects for strongly nonlinear disturbances are presented, helping to explain the observed resilience of eddy-transport barriers in the Jovian and terrestrial atmospheres. The main focus is on the important case where the nonlinear disturbances are vortices with core sizes ∼LD, the Rossby (deformation) length. Then a nonlinear shear-straining mechanism that seems significant for barrier resilience is the shear-induced disruption of vortex pairs. A sufficiently strong vortex pair, with PV anomalies ±Δqvortex, such that Δqvortex ≫ Δqbarrier, can of course punch through the barrier. There is a threshold for substantial penetration through the barrier, related to thresholds for vortex merging. Substantial penetration requires Δqvortex ≳ Δqbarrier, with an accuracy or fuzziness of order 10% when core size ∼LD, in a shallow-water quasigeostrophic model. It is speculated that, radiation stress permitting, the barrier-penetration threshold regulates jet spacing in a staircase situation. For instance, if a staircase is already established by stirring and if the stirring is increased to produce Δqvortex values well above threshold, then the staircase steps will be widened (for given background PV gradient β) until the barriers hold firm again, with Δqbarrier increased to match the new threshold. With the strongest-vortex core size ∼LD this argument predicts a jet spacing 2b = Δqbarrier/β ∼ L2Rh (Uvortex)/LD in order of magnitude, where LRh(Uvortex) = (Uvortex/β)1/2, the Rhines scale based on the peak vortex velocity Uvortex, when 2b ≳ LD. The resulting jet speeds Ujet are of the same order as Uvortex; thus also 2b ∼ L2Rh(Ujet)/LD. Weakly inhomogeneous turbulence theory is inapplicable here because there is no scale separation between jets and vortices, both having scales ∼LD in this situation.

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 Experimental Investigation of the Flow Field of Deep Rotating Stall in a Centrifugal Compressor

1994 ◽  
Author(s):  
Y. N. Chen ◽  
U. Seidel ◽  
J. Chen ◽  
U. Haupt ◽  
M. Rautenberg
Keyword(s):  
Rossby Wave ◽  
Centrifugal Compressor ◽  
Reverse Flow ◽  
Baroclinic Instability ◽  
Wave Theory ◽  
Polar Front ◽  
Rotating Stall ◽  
Squall Line ◽  
Two Dimensional ◽  
Pressure Pattern

The pressure field of deep rotating stall of a centrifugal compressor with two stall cells is analysed by means of the two-dimensional pressure pattern in the impeller determined by Chen et al. (1993). These authors transferred the pressure pattern measured on the shroud surface (i.e. in the absolute frame) to that related to the rotating blade channels. The transferred pressure pattern is thus a two-dimensional one. The existence of the low and high pressure vortices according to the Rossby wave theory is confirmed by this experiment. The development stages of the two vortices, in combination with the Rossby wave that steers the rotating stall, can be evaluated very well. The vortex low is developed from the front between the reverse flow (with high temperature and entropy) and the forward flow (with low temperature and entropy) due to baroclinic instability. Its center is situated within the channel of the splitter blade. This front is accompanied by a squall line of small-scaled eddies. This is the same phenomenon as can be observed on the meteorological polar front. The vortex high is induced by the vortex low. Its embryo starts on the pressure surface. Its center is situated behind the inlet edge of the splitter blade. It can be further verified that the stall cell is caused by the backflows of the induction fields of the two vortices (low and high).

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