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Carnevale, GF, Kloosterziel RC, Orlandi P.  2016.  Equilibration of centrifugally unstable vortices: A review. European Journal of Mechanics B-Fluids. 55:246-258.   10.1016/j.euromechflu.2015.06.007   AbstractWebsite

In three-dimensional flow, a vortex can become turbulent and be destroyed through a variety of instabilities. In rotating flow, however, the result of the breakup of a vortex is usually a state comprising several vortices with their axes aligned along the ambient rotation direction. This article is a review of our recent work on how the combined effect of centrifugal and barotropic instabilities can breakup a vortex and lead to its reformation in a predictable way even though an intermediate stage in the evolution is turbulent. Centrifugal instability tends to force the unstable vortex into a turbulent state that mixes absolute angular momentum in such a way as to precondition the flow for a subsequent barotropic instability. A method for predicting the redistribution of angular momentum and theresulting velocity profile is discussed. The barotropic instability horizontally redistributes the component of vorticity that is aligned along the ambient rotation vector, resulting in the final byproducts of the instability, which are stabilized by the effects of ambient rotation. A prediction scheme that puts the tendencies of these two instabilities together proves to be very reliable. (C) 2015 Elsevier Masson SAS. All rights reserved.

Espa, S, Cenedese A, Mariani M, Carnevale GF.  2009.  Quasi-two-dimensional flow on the polar beta-plane: Laboratory experiments. Journal of Marine Systems. 77:502-510.   10.1016/j.jmarsys.2008.10.015   AbstractWebsite

Geophysical turbulence is strongly affected by the variation of the Coriolis parameter with latitude. This variation results in the so-called beta-effect, which forces energy from small-scales to be transferred preferentially into zonal motions. This effect results in the formation of narrow jet-like zonal flows that dominate the dynamics and act as transport barriers. Here, laboratory experiments are used to reproduce this effect in decaying turbulent flows. An electromagnetic cell is used to generate an initial field of vorticity in a rotating tank. Under conditions of quasigeostrophic flow, the beta-effect is produced by depth variation of the flow instead of variation of the Coriolis parameter. The effects of changing the container geometry and the overall fluid depth on the production of jets are investigated. The results suggest that this laboratory configuration can be used to model jet formation in the oceans and that increasing fluid depth is a practical way to decrease viscous effects. (C) 2008 Elsevier B.V. All rights reserved.

Orlandi, P, Carnevale GF.  1999.  Evolution of isolated vortices in a rotating fluid of finite depth. Journal of Fluid Mechanics. 381:239-269.   10.1017/s0022112098003693   AbstractWebsite

Laboratory experiments have shown that monopolar isolated vortices in a rotating flow undergo instabilities that result in the formation of multipolar vortex states such as dipoles and tripoles. In some cases the instability is entirely two-dimensional, with the vortices taking the form of vortex columns aligned along the direction of the ambient rotation at all times. In other cases, the vortex first passes through a highly turbulent three-dimensional state before eventually reorganizing into vortex columns. Through a series of three-dimensional numerical simulations, the roles that centrifugal instability, barotropic instability, and the bottom Ekman boundary layer play in these instabilities are investigated. Evidence is presented that the centrifugal instability can trigger the barotropic instabilities by the enhancement of vorticity gradients. It is shown that the bottom Ekman layer is not essential to these instabilities but can strongly modify their evolution.

Kloosterziel, RC, Carnevale GF, Philippe D.  1993.  Propagation of barotropic dipoles over topography in a rotating tank. Dynamics of Atmospheres and Oceans. 19:65-100.   10.1016/0377-0265(93)90032-3   AbstractWebsite

It is shown how symmetric dipolar vortices can be formed by the action of an impulsive jet in a homogeneous single layer of fluid in a rotating tank. These dipoles are allowed to interact with a constant topographic slope, which can model a beta-plane or a continental shelf. A dipole's trajectory bends toward the right when climbing a slope and to the left when descending, as predicted by numerical simulations and analytical arguments. The maximum penetration of the dipoles over a slope, the adjustment to the slope, and formation of trailing lobes are compared with both numerical simulations and a two-point vortex model. The results suggest that Rossby wave radiation plays an important role in the interaction process.

Carnevale, GF, McWilliams JC, Pomeau Y, Weiss JB, Young WR.  1991.  Evolution of vortex statistics in two-dimensional turbulence. Physical Review Letters. 66:2735-2737.   10.1103/PhysRevLett.66.2735   AbstractWebsite

Freely evolving two-dimensional turbulence is dominated by coherent vortices. The density of these vortices decays in time as rho approximately t^-ɛ with ɛ almost-equal-to 0.75. A new scaling theory is proposed which expresses all statistical properties in terms of ɛ. Thus the average circulation of the vortices increases as t^ɛ/2 and their average radius as t^ɛ/4. The total energy is constant, the enstrophy decreases as t^ɛ/2, and the vorticity kurtosis increases as t^ɛ/2. These results are supported both by numerical simulations of the fluid equations and by solutions of a modified point-vortex model.

Carnevale, GF, Cavazza P, Orlandi P, Purini R.  1991.  An explanation for anomalous vortex merger in rotating‐tank experiments. Physics of Fluids a-Fluid Dynamics. 3:1411-1415.   10.1063/1.858019   AbstractWebsite

Theory and simulations based on the two-dimensional Euler equation predict a critical distance of separation for the merger of two like-signed vortices. By the symmetry of the equation, this separation must be the same for both cyclone and anticyclone pairs. In rotating-tank experiments, the observed critical separation distance for anticyclone merger is in accord with predictions; however, pairs of cyclones have been found to merge in all cases examined, even with separations substantially greater than the predicted critical separation. The hypothesis that this discrepancy is due to the presence of Ekman volume fluxes, which are not incorporated in the two-dimensional theory, is examined and found not quantitatively supportable. A second hypothesis is that the parabolic curvature of the free upper surface of the fluid in the rotating tank induces motion of the cyclones toward the center of the tank and hence promotes the cyclone pair merger. Quasigeostrophic simulations which capture this "topography effect" show good agreement with the rotating-tank experiments.