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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.

Carnevale, GF, Kloosterziel RC, Orlandi P, van Sommeren D.  2011.  Predicting the aftermath of vortex breakup in rotating flow. Journal of Fluid Mechanics. 669:90-119.   10.1017/s0022112010004945   AbstractWebsite

A method for predicting the outcome of vortex breakup in a rotating flow is introduced. The vortices dealt with here are subject to both centrifugal and barotropic instabilities. The prediction of the aftermath of the breakup relies on knowing how both centrifugal and barotropic instabilities would equilibrate separately. A theoretical model for non-linear equilibration in centrifugal instability is wedded to two-dimensional simulation of barotropic instability to predict the final vortices that emerge from the debris of the original vortex. This prediction method is tested against three-dimensional Navier-Stokes simulations. For vortices in which a rapid centrifugal instability triggers a slower barotropic instability, the method is successful both qualitatively and quantitatively. The skill of the prediction method decreases as the time scales of the two instabilities become comparable.

Zavala Sanson, L, Serravall R, Carnevale GF, vanHeijst GJF.  2005.  Experiments and simulations on coastal flows in the presence of a topographic slope. Journal of Physical Oceanography. 35:2204-2218.   10.1175/jpo2815.1   AbstractWebsite

The evolution of a barotropic coastal current in the presence of a bottom ramp-shaped topography is studied by means of laboratory experiments and numerical simulations. The experiments are performed in a rectangular rotating tank filled with freshwater. The fluid depth is shallow at one side of the domain and deeper at the other side, and both regions are divided by a narrow slope, whose depth contours are perpendicular to the long sides of the tank. A current approaching the slope is produced along one of the vertical walls, having the boundary at its right. Two configurations are analyzed: when the current flows from shallow to deep water and when flowing in the opposite direction. In the first scenario, the current is divided in two parts, one of them following the coastline. The other part of the current pairs with a cell of negative relative vorticity generated at the slope due to squeezing effects, forming a dipolar structure moving offshore, back toward the shallow side. In addition, a weak current moving inshore along the slope is clearly formed. In the second configuration, when the flow goes from deep to shallow water, a part of or even the whole current might be forced to move along the contours of the topography, away from the coast. In this case there is no dipole formation. The experiments are well reproduced by means of quasigeostrophic numerical simulations, which allow a more detailed systematic study of the influence of flow parameters such as the topography height and the width of the slope.

Carnevale, GF, Briscolini M, Orlandi P.  2001.  Buoyancy- to inertial-range transition in forced stratified turbulence. Journal of Fluid Mechanics. 427:205-239.   10.1017/s002211200000241x   AbstractWebsite

The buoyancy range, which represents a transition from large-scale wave-dominated motions to small-scale turbulence in the oceans and the atmosphere, is investigated through large-eddy simulations. The model presented here uses a continual forcing based on large-scale standing internal waves and has a spectral truncation in the isotropic inertial range. Evidence is presented for a break in the energy spectra from the anisotropic k(-3) buoyancy range to the small-scale k(-5/3) isotropic inertial range. Density structures that form during wave breaking and periods of high strain rate are analysed. Elongated vertical structures produced during periods of strong straining motion are found to collapse in the subsequent vertically compressional phase of the strain resulting in a zone or patch of mixed fluid.

Carnevale, GE, Smith SGL, Crisciani F, Purini R, Serravall R.  1999.  Bifurcation of a coastal current at an escarpment. Journal of Physical Oceanography. 29:969-985.   10.1175/1520-0485(1999)029<0969:boacca>;2   AbstractWebsite

The evolution of a coastal current as it encounters an escarpment depends strongly on whether the geometry of the coast and escarpment is right or left "handed," independent of the direction of the coastal current. Handedness is defined such that right-handed means that when looking across the escarpment from the deep to the shallow side, the coast is found on the right. The essential aspects of the difference in behavior of the current in the two geometries are captured by a simple quasigeostrophic model of coastal flow over a step. An exact analytic solution to the nonlinear stationary problem is obtained. This solution shows that, when a coastal current crosses an escarpment in the left-handed geometry, the speed of the current will increase independent of whether the flow is from shallow to deep or from deep to shallow. For the right-handed geometry, the speed of the current decreases, also independent of the direction of the coastal flow. In the left (right)-handed geometry, there is associated to the coastal flow an inshore (offshore) current along the escarpment. These results are explained in terms of linear wave theory and vortex dynamics. Numerical simulations are used to examine the evolution of the flow from the initial encounter to the establishment of a stationary flow. The relevance of this research is discussed in light of recent results from laboratory experiments and oceanic observations.

Carnevale, GF, Briscolini M, Kloosterziel RC, Vallis GK.  1997.  Three-dimensionally perturbed vortex tubes in a rotating flow. Journal of Fluid Mechanics. 341:127-163.   10.1017/s0022112097005430   AbstractWebsite

Numerical experiments are used to study the evolution of perturbed vortex tubes in a rotating environment in order to better understand the process of two-dimensionalization of unsteady rotating flows. We specifically consider non-axisymmetric perturbations to columnar vortices aligned along the axis of rotation. The basic unperturbed vortex is chosen to have a Gaussian cross-sectional vorticity distribution. The experiments cover a parameter space in which both the strength of the initial perturbation and the Rossby number are varied. The Rossby number is defined here as the ratio of the maximum amplitude of vorticity in the Gaussian vorticity profile to twice the ambient rotation rate. For small perturbations and small Rossby numbers, both cyclones and anticyclones behave similarly, relaxing rapidly back toward two-dimensional columnar vortices. For large perturbations and small Rossby numbers, a rapid instability occurs for both cyclones and anticyclones in which antiparallel vorticity is created. The tubes break up and then re-form again into columnar vortices parallel to the rotation axis (i.e. into a quasi-two-dimensional flow) through nonlinear processes. For Rossby numbers greater than 1, even small perturbations result in the complete breakdown of the anticyclonic vortex through centrifugal instability, while cyclones remain stable. For a range of Rossby numbers greater than 1, after the breakdown of the anticyclone, a new weaker anticyclone forms, with a small-scale background vorticity of spectral shape given approximately by the -5/3 energy spectral law.

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, Kloosterziel RC, vanHeijst GJF.  1991.  Propagation of barotropic vortices over topography in a rotating tank. Journal of Fluid Mechanics. 233:119-139.   10.1017/s0022112091000411   AbstractWebsite

A small-scale cyclonic vortex in a relatively broad valley tends to climb up and out of the valley in a cyclonic spiral about the centre, and when over a relatively broad hill it tends to climb toward the top in an anticyclonic spiral around the peak. This phenomenon is examined here through two-dimensional numerical simulations and rotating-tank experiments. The basic mechanism involved is shown to be the same as that which accounts for the northwest propagation of cyclones on a beta-plane. This inviscid nonlinear effect is also shown to be responsible for the observed translationary motion of barotropic vortices in a free-surface rotating tank. The behaviour of isolated vortices is contrasted with that of vortices with non-vanishing circulation.