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

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.

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).

Modal Interpretation for the Ekman Destabilization of Inviscidly Stable Baroclinic Flow in the Phillips Model

2010 ◽  
Vol 40 (4) ◽  
pp. 830-839 ◽  
Author(s):  
Gordon E. Swaters
Keyword(s):  
Phase Velocity ◽  
Boundary Layers ◽  
Rossby Wave ◽  
Classical Theory ◽  
Baroclinic Instability ◽  
Ekman Layer ◽  
Modal Interpretation ◽  
Phase Velocities ◽  
Phillips Model ◽  
Baroclinic Flow

Abstract Ekman boundary layers can lead to the destabilization of baroclinic flow in the Phillips model that, in the absence of dissipation, is nonlinearly stable in the sense of Liapunov. It is shown that the Ekman-induced instability of inviscidly stable baroclinic flow in the Phillips model occurs if and only if the kinematic phase velocity associated with the dissipation lies outside the interval bounded by the greatest and least neutrally stable Rossby wave phase velocities. Thus, Ekman-induced destabilization does not correspond to a coalescence of the barotropic and baroclinic Rossby modes as in classical inviscid baroclinic instability. The differing modal mechanisms between the two instability processes is the reason why subcritical baroclinic shears in the classical theory can be destabilized by an Ekman layer, even in the zero dissipation limit of the theory.

scholarly journals The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

2005 ◽  
Vol 131 (608) ◽  
pp. 1425-1440 ◽  
Author(s):  
J. Methven ◽  
B. J. Hoskins ◽  
E. Heifetz ◽  
C. H. Bishop
Keyword(s):  
Rossby Wave ◽  
Baroclinic Instability ◽  
Life Cycles

scholarly journals Balancing the Potential Vorticity Seesaw: The Bare Essentials of Baroclinic Instability

2019 ◽  
Vol 3 (3) ◽  
pp. 341-351
Author(s):  
Enda O’Brien
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Phase Locking ◽  
Baroclinic Instability ◽  
Mechanistic Explanation ◽  
Atmospheric Model ◽  
Key Characteristics ◽  
Background Temperature ◽  
Pv Gradient

Abstract This paper bypasses the mathematical technicalities of baroclinic instability and tries to provide a more conceptual, mechanistic explanation for a phenomenon that is fundamentally important to the dynamics of the earth’s atmosphere and oceans. The standard conceptual picture of baroclinic instability is reviewed and stripped down to identify the most essential features. These are: (a) Regions with both positive and negative potential vorticity (PV) gradients, (b) separate Rossby wave perturbations in each region where PV gradients are of different signs, and (c) cooperative phase locking between Rossby waves in regions of opposite PV gradient, which renders them stationary, and allows them to amplify to reduce the background temperature gradient (or baroclinicity) while still conserving total PV. These three factors constitute the “counterpropagating Rossby wave” perspective, and suggest the heuristic picture of a “PV seesaw”, which remains balanced as the instabilities (i.e., the phase-locked PV wave perturbations) grow out along opposite limbs. After reviewing the key characteristics of PV and Rossby waves, the process is illustrated by the spontaneous onset of baroclinic instability during spin-up of the Held–Suarez dynamical core atmospheric model.

Utility of Hovmöller diagrams to diagnose Rossby wave trains

2011 ◽  
Author(s):  
Ilona Glatt ◽  
Andreas Dörnbrack ◽  
Sarah Jones ◽  
Julia Keller ◽  
O. Martius ◽  
...  
Keyword(s):  
Rossby Wave ◽  
Wave Trains
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