scholarly journals The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

2008 ◽  
Vol 65 (8) ◽  
pp. 2498-2521 ◽  
Author(s):  
David A. Schecter
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Formal Theory ◽  
Resonant Absorption ◽  
Critical Layer ◽  
Wave Radiation ◽  
Rossby Number ◽  
Mean Flow ◽  
Surface Drag ◽  
Isentropic Coordinates

Abstract This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed. The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

scholarly journals The Structure of Baroclinic Modes in the Presence of Baroclinic Mean Flow

2020 ◽  
Vol 50 (1) ◽  
pp. 239-253
Author(s):  
K. H. Brink ◽  
J. Pedlosky
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Vertical Structure ◽  
Horizontal Gradient ◽  
Mean Flow ◽  
Stable Mode ◽  
Oceanic Current ◽  
Unstable Solutions ◽  
Rossby Wave Propagation ◽  
Baroclinic Modes

AbstractThis contribution seeks to understand the vertical structure of linearized quasigeostrophic baroclinic modes when they are modified by the presence of a baroclinic mean flow and associated potential vorticity gradients. It is found that even modest, O(0.05 m s−1), mean flows can give rise to very substantial changes in modal structures, often in the sense of increased surface intensification. The extent to which stable modes are modified depends strongly on the direction of Rossby wave propagation. Further, baroclinically unstable solutions can appear, and a meaningful inviscid critical-layer solution can occur at the transition to instability when the horizontal gradient of potential vorticity changes sign at some depth within the water column. In addition, the gravest, n = 0, vertical stable mode is no longer strictly barotropic, but rather it can carry density variability at frequencies much higher than those possible for baroclinic (higher) Rossby wave modes. This finding appears to be consistent with oceanic current-meter observations that suggest temperature variability propagation even when the frequency is too high for traditional baroclinic Rossby waves to exist.

Waves in a Cloudy Vortex

2007 ◽  
Vol 64 (2) ◽  
pp. 314-337 ◽  
Author(s):  
David A. Schecter ◽  
Michael T. Montgomery
Keyword(s):  
Rossby Wave ◽  
Small Amplitude ◽  
Rossby Waves ◽  
Wave Radiation ◽  
Rossby Number ◽  
System Of Equations ◽  
Discrete Vortex ◽  
Wave Dynamics ◽  
Cloud Coverage ◽  
Vortex Rossby Wave

Abstract This paper derives a system of equations that approximately govern small-amplitude perturbations in a nonprecipitating cloudy vortex. The cloud coverage can be partial or complete. The model is used to examine moist vortex Rossby wave dynamics analytically and computationally. One example shows that clouds can slow the growth of phase-locked counter-propagating vortex Rossby waves in the eyewall of a hurricane-like vortex. Another example shows that clouds can (indirectly) damp discrete vortex Rossby waves that would otherwise grow and excite spiral inertia–gravity wave radiation from a monotonic cyclone at high Rossby number.

scholarly journals Dynamical properties of vortical structures on the beta-plane

1994 ◽  
Vol 268 ◽  
pp. 103-131 ◽  
Author(s):  
G. G. Sutyrin ◽  
J. S. Hesthaven ◽  
J. P. Lynov ◽  
J. Juul Rasmussen
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Fluid Transport ◽  
Numerical Solutions ◽  
Critical Value ◽  
Wave Radiation ◽  
Approximate Theory ◽  
Initial Direction ◽  
Vortical Structures ◽  
Long Time

The long-time evolution of monopolar and dipolar vortices influenced by the largescale gradient of the ambient potential vorticity (the β-effect) is studied by direct numerical solutions of the equivalent barotropic quasi-geostrophic equation. Translation and reorganization of vortical structures are shown to depend strongly on their intensity. Transport of trapped fluid by vortical structures is illustrated by calculating particle trajectories and by considering closed isolines of potential vorticity and the streamfunction in a co-moving reference frame.The initial behaviour of strong monopoles is found to be well described by a recent approximate theory for the evolution of azimuthal mode one, even for times longer than the linear Rossby wave period. In the long-time limit, strong monopoles transport particles mainly westward, although the meridional displacement is several times larger than the initial vortex size. The appearance of an annulus with opposite radial gradient of the potential vorticity around the vortex core is demonstrated. This annulus forms owing to the meridional vortex drift on the β-plane and results in reorganization of a strong monopolar vortex into a rotating tripole. A critical value of the vortex intensity is found, below which the tripolar structure does not appear even in the case of an initially shielded vortex. Weak monopolar vortices are able to trap particles and provide some west-meridional fluid transport, even in the case when they decay like a linear Rossby wave packet.The evolution of initial f-plane dipoles on the β-plane is strongly dependent on the initial direction of propagation. Strong dipoles adjust to steadily propagating modon solutions either accelerating (westward case), decelerating (eastward case) or oscillating with a decaying amplitude (meridional case), thereby carrying trapped particles predominantly eastward. A steady state is not reached if the dipole intensity is below a critical value which depends on the initial direction of propagation. Weak dipoles either decay and shrink owing to Rossby wave radiation (westward case), gradually separate and split (eastward case), or disintegrate (meridional case) without longdistance fluid transport. Thus, on the β-plane monopoles provide mainly westward transport of trapped fluid, whereas dipoles provide mainly eastward transport. Only strong monopoles are found to provide significant meridional fluid transport.

scholarly journals The decay of cyclonic eddies by Rossby wave radiation

1998 ◽  
Vol 361 ◽  
pp. 237-252 ◽  
Author(s):  
N. ROBB McDONALD
Keyword(s):  
Shallow Water ◽  
Explicit Expression ◽  
Energy Flux ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Phase Speed ◽  
Wave Radiation ◽  
Conservation Of Energy ◽  
Radiation Induced ◽  
General Method

It is argued that because shallow water cyclones on a β-plane drift westward at a speed equal to an available Rossby wave phase speed, they must radiate energy and cannot, therefore, be steady. The form of the Rossby wave wake accompanying a quasi-steady cyclone is calculated and the energy flux in the radiated waves determined. Further, an explicit expression for the radiation-induced northward drift of the cyclone is obtained. A general method for determining the effects of the radiation on the radius and amplitude of the vortex based on conservation of energy and potential vorticity is given. An example calculation for a cyclone with a ‘top-hat’ profile is presented, demonstrating that the primary effect of the radiation is to decrease the radius of the vortex. The dimensional timescale associated with the decay of oceanic vortices is of the order of several months to a year.

scholarly journals The merger of geophysical vortices at finite Rossby and Froude number

2018 ◽  
Vol 848 ◽  
pp. 388-410 ◽  
Author(s):  
Jean N. Reinaud ◽  
David G. Dritschel
Keyword(s):  
Froude Number ◽  
Gravity Wave ◽  
Potential Vorticity ◽  
Initial Conditions ◽  
The Other ◽  
Vertical Shear ◽  
Wave Radiation ◽  
Rossby Number ◽  
Other Hand ◽  
Vorticity Anomaly

We investigate the merger of two co-rotating geophysical vortices at finite Rossby and Froude number. The initial conditions consist of two uniform potential vorticity vortices in near-equilibrium and in a nearly ‘balanced’ state (i.e. with negligible emission of inertia–gravity wave radiation). We determine the critical merger distance between the two vortices. This distance is found to increase with the magnitude of the Rossby number: intense cyclones or intense anticyclones are able to merge from further apart compared to weaker cyclones and anticyclones. Note that the Froude number is proportional to the Rossby number for the near-equilibrium initial conditions considered. The critical merging distance also depends on the sign of the potential vorticity anomaly, which is positive for ‘cyclones’ and negative for ‘anticyclones’. We show that ageostrophic motions occurring at finite Rossby number tend to draw cyclones together but draw anticyclones apart. On the other hand, we show that anticyclones tend to deform more, in particular when subject to vertical shear (as when the vortices are vertically offset). These two effects compete. Overall, nearly aligned cyclones tend to merge from further apart than their anticyclonic counterparts, while vertically offset anticyclones merge from further apart than cyclones.

Intense vortex motion in a stratified fluid on the beta-plane: an analytical theory and its validation

1997 ◽  
Vol 336 ◽  
pp. 203-220 ◽  
Author(s):  
GEORGI G. SUTYRIN ◽  
YVES G. MOREL
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Vortex Core ◽  
Vortex Motion ◽  
Relative Displacement ◽  
Analytical Theory ◽  
Wave Radiation ◽  
Layer Model ◽  
Beta Plane ◽  
Constant Potential

This paper deals with the self-induced translation of intense vortices on the β-plane in the framework of the multi-layer quasi-geostrophic approximation. An analytical theory is presented and compared to numerical experiments. To predict the vortex trajectories, we consider initially monopolar vortices, with a core of piecewise-constant potential vorticity, and calculate the evolution of the dipolar circulation which advects the vortex core. This multi-layer model yields analytical solutions for a period while the Rossby wave radiation is small.The development of the dipolar circulation and corresponding vortex translation are described as the results of three effects. The first and second are similar to what was found in earlier studies with a one-layer model: advection of the planetary vorticity by the symmetric vortex circulation, and horizonal deformations of the vortex core. In addition, when stratification is taken into account, the vertical tilting of the vortex core also plays a role. This third effect is here represented by the relative displacement of potential vorticity contours in different layers.Examples are given for one-, two- and three-layer models and compared with numerical simulations. It is found that the analytical predictions are good for several Rossby wave periods.

A Climatology of Rossby Wave Breaking on the Southern Hemisphere Tropopause

2011 ◽  
Vol 68 (4) ◽  
pp. 798-811 ◽  
Author(s):  
Thando Ndarana ◽  
Darryn W. Waugh
Keyword(s):  
Southern Hemisphere ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Seasonal Variations ◽  
Wave Breaking ◽  
Polar Front ◽  
Rossby Wave Breaking ◽  
South Pacific Ocean ◽  
Ocean Region ◽  
Summer Minimum

Abstract A 30-yr climatology of Rossby wave breaking (RWB) on the Southern Hemisphere (SH) tropopause is formed using 30 yr of reanalyses. Composite analysis of potential vorticity and meridional fluxes of wave activity show that RWB in the SH can be divided into two broad categories: anticyclonic and cyclonic events. While there is only weak asymmetry in the meridional direction and most events cannot be classified as equatorward or poleward in terms of the potential vorticity structure, the position and structure of the fluxes associated with equatorward breaking differs from those of poleward breaking. Anticyclonic breaking is more common than cyclonic breaking, except on the lower isentrope examined (320 K). There are marked differences in the seasonal variations of RWB on the two surfaces, with a winter minimum for RWB around 350 K but a summer minimum for RWB around 330 K. These seasonal variations are due to changes in the location of the tropospheric jets and dynamical tropopause. During winter the subtropical jet and tropopause at 350 K are collocated in the Australian–South Pacific Ocean region, resulting in a seasonal minimum in the 350-K RWB. During summer the polar front jet and 330-K tropopause are collocated over the Southern Atlantic and Indian Oceans, inhibiting RWB in this region.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

Method for Identifying and Clustering Rossby Wave Breaking Events in the Northern Hemisphere

2021 ◽  
pp. 17-28
Author(s):  
A. V. Gochakov ◽  
◽  
O. Yu. Antokhina ◽  
V. N. Krupchatnikov ◽  
Yu. V. Martynova ◽  
...  
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Wave Breaking ◽  
Large Scale ◽  
Method Development ◽  
Spatial Clustering ◽  
Potential Temperature ◽  
Reanalysis Data ◽  
Rossby Wave Breaking ◽  
Dynamic Phenomena

Many large-scale dynamic phenomena in the Earth’s atmosphere are associated with the processes of propagation and breaking of Rossby waves. A new method for identifying the Rossby wave breaking (RWB) is proposed. It is based on the detection of breakings centers by analyzing the shape of the contours of potential vorticity or temperature on quasimaterial surfaces: isentropic and iserthelic (surfaces of constant Ertel potential vorticity (PV)), with further RWB center clustering to larger regions. The method is applied to the set of constant PV levels (0.3 to 9.8 PVU with a step of 0.5 PVU) at the level of potential temperature of 350 K for 12:00 UTC. The ERA-Interim reanalysis data from 1979 to 2019 are used for the method development. The type of RWB (cyclonic/anticyclonic), its area and center are determined by analyzing the vortex geometry at each PV level for every day. The RWBs obtained at this stage are designated as elementary breakings. Density-Based Spatial Clustering of Applications with Noise algorithm (DBSCAN) was applied to all elementary breakings for each month. As a result, a graphic dataset describing locations and dynamics of RWBs for every month from 1979 to 2019 is formed. The RWB frequency is also evaluated for each longitude, taking into account the duration of each RWB and the number of levels involved, as well as the anomalies of these parameters.

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