scholarly journals Rossby wave radiation by an eddy on a beta-plane: Experiments with laboratory altimetry

2015 ◽  
Vol 27 (7) ◽  
pp. 076604 ◽  
Author(s):  
Y. Zhang ◽  
Y. D. Afanasyev
Keyword(s):  
Rossby Wave ◽  
Wave Radiation ◽  
Beta Plane

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.

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 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 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.

Barotropic annular flows, vortices and waves on a beta cone

2019 ◽  
Vol 875 ◽  
pp. 225-253 ◽  
Author(s):  
Michael Rabinovich ◽  
Ziv Kizner ◽  
Glenn Flierl
Keyword(s):  
Rossby Waves ◽  
Bottom Topography ◽  
Wave Radiation ◽  
Unstable Flow ◽  
Flat Bottom ◽  
Azimuthal Mode ◽  
Initial Flow ◽  
Beta Plane ◽  
Beta Effect ◽  
Annular Flows

We consider two-dimensional quasi-geostrophic annular flows around a circular island with a radial offshore bottom slope. Since the conical bottom topography causes a certain beta effect, by analogy with the conventional beta plane we term our model a beta cone. Our focus is on the flows with zero total circulation, which are composed of two concentric rings of uniform potential vorticity (PV) attached to the island. The linear stability of such flows on a beta cone was investigated in a previous publication of ours. In the present paper, we study numerically the nonlinear evolution of weakly viscous flows, whose parameters are fitted so as to guarantee the highest instability of the azimuthal mode $m=1,\ldots ,6$. We study the production of vortices and Rossby waves due to the instability, consider the effect of waves on the emerging vortices and the interaction between the vortices. As in the flat-bottom case, at $m\geqslant 2$, the instability at weak bottom slopes normally leads to the emission of $m$ dipoles. However, a fundamental difference between the flat-bottom and beta-cone cases is observed in the trajectories of the dipoles as the latter recede from the island. When the flow is initially counterclockwise, the conical beta effect may force the dipoles to make a complete turn, come back to the island and rearrange in new couples that again leave the island and return. This quasi-periodic process gradually fades due to filamentation, wave radiation and viscous dissipation. Another possible outcome is symmetrical settling of $m$ dipoles in a circular orbit around the island, in which they move counterclockwise. This behaviour is reminiscent of the adaptation of strongly tilted beta-plane modons (dipoles) to the eastward movement. If the initial flow is clockwise, the emerged dipoles usually disintegrate, but sometimes, the orbital arrangement is possible. At a moderate slope, the evolution of an unstable flow, which is initially clockwise, may end up in the formation of a counterclockwise flow. At steeper slopes, a clockwise flow may transform into a quasi-stationary vortex multipole. When the slope is sufficiently steep, the topographic Rossby waves developing outside of the PV rings can smooth away the instability crests and troughs at the outer edge of the main flow, thus preventing the vortex production but allowing the formation of a new quasi-stationary pattern, a doubly connected coherent PV structure possessing $m$-fold symmetry. Such an $m$-fold pattern can be steady only if it rotates counterclockwise, otherwise it radiates Rossby waves and transforms eventually into a circularly symmetric flow.

scholarly journals Dynamics of monopolar vortices on a topographic beta-plane

2002 ◽  
Vol 456 ◽  
pp. 353-376 ◽  
Author(s):  
J.-B. FLÓR ◽  
I. EAMES
Keyword(s):  
Rossby Wave ◽  
Vortex Dynamics ◽  
Lift Force ◽  
Wave Speed ◽  
Rossby Waves ◽  
Mechanistic Model ◽  
Radial Distance ◽  
Azimuthal Velocity ◽  
Beta Plane ◽  
Translational Speed

The dynamics of a cyclonic monopolar vortex on a topographic beta-plane are studied experimentally and theoretically. Detailed measurements of the vortex structure are conducted using high-resolution quantitative velocity measurements. The initial velocity profiles were described in terms of a radius Rvm, maximum azimuthal velocity vθm, and a dimensionless parameter α which characterizes the steepness of the velocity profile. The initial direction of motion of the monopolar vortex is critically dependent on α and weakly dependent of the initial strength and size of the vortex: isolated vortices (α ∼ 3) move north, whereas non-isolated vortices characterized by α ∼ 1 move northwest. When the azimuthal velocity decays slowly with radial distance (α < 1.4), Rossby wave generation dominates the vortex dynamics and the translational speed of the vortex correlates with the Rossby wave speed. When the azimuthal velocity decays rapidly with radial distance (α > 1.4) the vortex is isolated and the translational speed is much slower than the Rossby wave speed. To interpret the effect of the vortex structure on the direction of motion, a mechanistic model is developed which includes the Rossby force and a lift force arising from circulation around the vortex, but does not include the effect of Rossby waves. The Rossby force results from the integrated effect of the Coriolis force on the vortex and drives the vortex north; the lift force is determined from the circulation around the vortex and drives the vortex west. Comparison with the experimental data reveals two regimes: α < 1.4, where the vortex dynamics are dominated by Rossby waves whereas for α > 1.4 Rossby waves are weak and favourable agreement is found with the mechanistic model.

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