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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.

Weiss, J, Tabor M, Carnevale G.  1983.  The Painlevé property for partial differential equations. Journal of Mathematical Physics. 24:522-526.   10.1063/1.525721   AbstractWebsite

In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well‐known partial differential equations (Burgers’ equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.

Verzicco, R, Orlandi P, Eisenga AHM, vanHeijst GJF, Carnevale GF.  1996.  Dynamics of a vortex ring in a rotating fluid. Journal of Fluid Mechanics. 317:215-239.   10.1017/s0022112096000730   AbstractWebsite

The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier-Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a 'degree of polarization'. If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown. Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.

Vallis, GK, Carnevale GF, Young WR.  1989.  Extremal energy properties and construction of stable solutions of the Euler equations. Journal of Fluid Mechanics. 207:133-152.   10.1017/s0022112089002533   AbstractWebsite

Certain modifications of the Euler equations of fluid motion lead to systems in which the energy decays or grows monotonically, yet which preserve other dynamically important characteristics of the field. In particular, all topological invariants associated with the vorticity field are preserved. In cases where isolated energy extrema exist, a stable steady flow can be found. In two dimensions, highly constrained by vorticity invariants, it is shown that the modified dynamics will lead to at least one non-trivial stationary, generally stable, solution of the equations of motion from any initial conditions. Numerical implementation of the altered dynamics is straightforward, and thus provides a practical method for finding stable flows. The method is sufficiently general to be of use in other dynamical systems.Insofar as three-dimensional turbulence is characterized by a cascade of energy, but not topological invariants, from large to small scales, the procedure has direct physical significance. It may be useful as a parameterization of the effects of small unresolved scales on those explicitly resolved in a calculation of turbulent flow.

Orlandi, P, Carnevale GF.  2007.  Nonlinear amplification of vorticity in inviscid interaction of orthogonal Lamb dipoles. Physics of Fluids. 19   10.1063/1.2732438   AbstractWebsite

Dynamical arguments based on the structure of the Euler equations suggest the possibility of rapid amplification of vorticity in which the vorticity and the rate of strain grow proportionately. During such growth, the vorticity is expected to amplify as a (t(s)-t)(-1) power-law in time. This behavior is difficult to demonstrate numerically, in part, because initial transients tend to obscure it. Lamb dipoles are used here to construct the initial vorticity. This helps to avoid these transients and results in a flow exhibiting the expected power-law vorticity amplification for a period of time. The spatial region where the vorticity growth rate is maximal is investigated in detail using a decomposition of the vorticity along the principal axes of the rate-of-strain tensor. It is demonstrated that the vorticity and strain rate in one direction in this decomposition are proportional during the period of rapid vorticity growth. These findings suggest that, during this period, the Euler equations can be reduced to a one-dimensional model equation for vorticity in the rate-of-strain coordinate system. (C) 2007 American Institute of Physics.

Orlandi, P, Pirozzoli S, Bernardini M, Carnevale GF.  2014.  A minimal flow unit for the study of turbulence with passive scalars. Journal of Turbulence. 15:731-751.   10.1080/14685248.2014.927066   AbstractWebsite

The concept of a minimal flow unit (MFU) for the study of the basic physics of turbulent flows is introduced. The MFU is an initial vorticity configuration that consists of a few simple well-defined large-scale vortex structures. The form and position of these structures are chosen so that their interaction produces turbulence capturing many of the essential characteristics of isotropic homogeneous turbulence produced from random-phase initial conditions or that produced by continual random-phase forcing. The advantage of using the MFU is that the evolution of the vortex structures can be followed more clearly and the relationship between the evolving vortex structures and the various ranges in the energy spectrum can be more clearly defined. The addition of passive scalar fields to the MFU permits an investigation of passive scalar mixing that is relevant to the study of combustion. With a particular choice of the MFU, one that produces a trend to a finite-time singularity in the vorticity field, it is demonstrated that passive scalar distributed in the original large-scale vortices will develop intense gradients in the region where the vorticity is tending toward a singularity. In viscous flow, the evolution of the MFU clearly shows how the volume of the regions where originally well-separated passive scalars come into contact increases with increasing Reynolds number.

Orlandi, P, Carnevale GF, Lele SK, Shariff K.  2001.  Thermal perturbation of trailing vortices. European Journal of Mechanics B-Fluids. 20:511-524.   10.1016/s0997-7546(01)01131-1   AbstractWebsite

The possibility of diminishing the danger of trailing vortices through thermal forcing is investigated. It is shown that heating the vortices would have two beneficial effects. First, it would cause the vortices to descend more rapidly thus clearing the flight path more quickly. Second, it would cause the vortices to draw closer together, thus greatly increasing the growth rate of the short-wave instabilities that can ultimately destroy the vortices through cross-diffusion. (C) 2001 Editions scientifiques et medicales Elsevier SAS.

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.

Orlandi, P, Pirozzoli S, Carnevale GF.  2012.  Vortex events in Euler and Navier-Stokes simulations with smooth initial conditions. Journal of Fluid Mechanics. 690:288-320.   10.1017/jfm.2011.430   AbstractWebsite

We present high-resolution numerical simulations of the Euler and Navier-Stokes equations for a pair of colliding dipoles. We study the possible approach to a finite-time singularity for the Euler equations, and contrast it with the formation of developed turbulence for the Navier-Stokes equations. We present numerical evidence that seems to suggest the existence of a blow-up of the inviscid velocity field at a finite time (t(s)) with scaling vertical bar u vertical bar(infinity) similar to (t(s) - t)(-1/2), vertical bar omega vertical bar(infinity) similar to (t(s) - t)(-1). This blow-up is associated with the formation of a k(-3) spectral range, at least for the finite range of wavenumbers that are resolved by our computation. In the evolution toward t(s), the total enstrophy is observed to increase at a slower rate, Omega similar to (t(s) - t)(-3/4), than would naively be expected given the behaviour of the maximum vorticity, omega(infinity) similar to (t(s) - t)(-1). This indicates that the blow-up would be concentrated in narrow regions of the flow field. We show that these regions have sheet-like structure. Viscous simulations, performed at various Re, support the conclusion that any non-zero viscosity prevents blow-up in finite time and results in the formation of a dissipative exponential range in a time interval around the estimated inviscid t(s). In this case the total enstrophy saturates, and the energy spectrum becomes less steep, approaching k(-513). The simulations show that the peak value of the enstrophy scales as Re-3/2, which is in accord with Kolmogorov phenomenology. During the short time interval leading to the formation of an inertial range, the total energy dissipation rate shows a clear tendency to become independent of Re, supporting the validity of Kolmogorov's law of finite energy dissipation. At later times the kinetic energy shows a t(-1.2) decay for all Re, in agreement with experimental results for grid turbulence. Visualization of the vortical structures associated with the stages of vorticity amplification and saturation show that, prior to ts, large-scale and the small-scale vortical structures are well separated. This suggests that, during this stage, the energy transfer mechanism is non-local both in wavenumber and in physical space. On the other hand, as the spectrum becomes shallower and a k(-5/3) range appears, the energy-containing eddies and the small-scale vortices tend to be concentrated in the same regions, and structures with a wide range of sizes are observed, suggesting that the formation of an inertial range is accompanied by transfer of energy that is local in both physical and spectral space.

Koniges, AE, Crotinger JA, Dannevik WP, Carnevale GF, Diamond PH.  1991.  Equilibrium spectra and implications for a two‐field turbulence model. Physics of Plasmas. 3:1297-1299.   10.1063/1.859822   Abstract

Analytic expressions are given for statistical mechanical equilibrium solutions of two‐field turbulence model equations that are used in describing plasma drift waves and for passive scalar advection in a neutral fluid. These are compared with those previously proposed [Phys. Fluids B 1, 1331 (1989)], in particular regarding the role of the cross correlations between fields. Implications for two‐point closure calculations are discussed.

Kloosterziel, RC, Carnevale GF.  2003.  Closed-form linear stability conditions for magneto-convection. Journal of Fluid Mechanics. 490:333-344.   10.1017/s0022112003005329   AbstractWebsite

Chandrasekhar (1961) extensively investigated the linear dynamics of Rayleigh-Benard convection in an electrically conducting fluid exposed to a uniform vertical magnetic field and enclosed by rigid, stress-free, upper and lower boundaries. He determined the marginal stability boundary and critical horizontal wavenumbers for the onset of convection as a function of the Chandrasekhar number Q or Hartmann number squared. No closed-form formulae appeared to exist and the results were tabulated numerically. We have discovered simple expressions that concisely describe the stability properties of the system. When the Prandtl number Pr is greater than or equal to the magnetic Prandtl number Pm the marginal stability boundary is described by the curve Q = pi(-2)[R - (RcR2/3)-R-1/3] where R is the Rayleigh number and R-c = (27/4)pi(4) is Rayleigh's famous critical value for the onset of stationary convection in the absence of a magnetic field (Q = 0). When Pm > Pr the marginal stability boundary is determined by this curve until intersected by the curve Q = 1/pi(2)[Pm-2(1 + Pr)/Pr-2(1 + Pm)R - ((1 + Pr)(Pr + Pm)/Pr-2)(1/3) (Pm-2(1 + Pr)/Pr-2(1 + Pm))(2/3) (RcR2/3)-R-1/3]. An expression for the intersection point is derived and also for the critical horizontal wavenumbers for which instability sets in along the marginal stability boundary either as stationary convection or in an oscillatory fashion. A simple formula is derived for the frequency of the oscillations. Also we show that in the limit of vanishing magnetic diffusivity, or infinite electrical conductivity, the system is unstable for sufficiently large R. Instability in this limit always sets in via overstability.

Kloosterziel, RC, Carnevale GF, Orlandi P.  2017.  Equatorial inertial instability with full Coriolis force. Journal of Fluid Mechanics. 825:69-108.   10.1017/jfm.2017.377   AbstractWebsite

The zonally symmetric inertial instability of oceanic near-equatorial flows is studied through high-resolution numerical simulations. In homogeneous upper layers, the instability of surface-confined westward currents implies potentially fast downward mixing of momentum with a predictable final equilibrium. With increasing Reynolds number, latitudinal scales along the surface associated with the instability become ever smaller and initially the motions are ever more concentrated underneath the surface. The results suggest that even if the upper layer is stratified, it may still be necessary to include the full Coriolis force in the dynamics rather than use the traditional beta-plane approximation.

Kloosterziel, RC, Carnevale GF.  2007.  Generalized energetics for inertially stable parallel shear flows. Journal of Fluid Mechanics. 585:117-126.   10.1017/s0022112007006933   AbstractWebsite

For simple parallel shear flows on the f-plane and the equatorial beta-plane we derive an energy norm for zonally invariant perturbations. It is used to derive the linear stability boundary for when these flows are inertially stable in the classical sense but may be destabilized due to unequal rates of diffusion of momentum and heat. The analysis is valid when there are arbitrary, zonally invariant, no-slip boundaries which are perfect thermal conductors.

Kloosterziel, RC, Carnevale GF.  1999.  On the evolution and saturation of instabilities of two-dimensional isolated circular vortices. Journal of Fluid Mechanics. 388:217-257.   10.1017/s0022112099004760   AbstractWebsite

Laboratory observations and numerical experiments have shown that a variety of compound vortices can emerge in two-dimensional flow due to the instability of isolated circular vortices. The simple geometrical features of these compound vortices suggest that their description may take a simple form if an appropriately chosen set of functions is used. We employ a set which is complete on the infinite plane for vorticity distributions with finite total enstrophy. Through projection of the vorticity equation (Galerkin method) and subsequent truncation we derive a dynamical system which is used to model the observed behaviour in as simple as possible a fashion. It is found that at relatively low-order truncations the observed behaviour is qualitatively captured by the dynamical system. We determine what the necessary ingredients are for saturation of instabilities at finite amplitude in terms of wave-wave interactions and feedback between various azimuthal components of the vorticity field.

Kloosterziel, RC, Carnevale GF.  1992.  Formal stability of circular vortices. Journal of Fluid Mechanics. 242:249-278.   10.1017/s0022112092002362   AbstractWebsite

The second variation of a linear combination of energy and angular momentum is used to investigate the formal stability of circular vortices. The analysis proceeds entirely in terms of Lagrangian displacements to overcome problems that otherwise arise when one attempts to use Arnol'd's Eulerian formalism. Specific attention is paid to the simplest possible model of an isolated vortex consisting of a core of constant vorticity surrounded by a ring of oppositely signed vorticity. We prove that the linear stability regime for this vortex coincides with the formal stability regime. The fact that there are formally stable isolated vortices could imply that there are provable nonlinearly stable isolated vortices. The method can be applied to more complicated vortices consisting of many nested rings of piecewise-constant vorticity. The equivalent expressions for continuous vorticity distributions are also derived.

Kloosterziel, RC, Carnevale GF.  2003.  Closed-form linear stability conditions for rotating Rayleigh-Benard convection with rigid stress-free upper and lower boundaries. Journal of Fluid Mechanics. 480:25-42.   10.1017/s0022112002003294   AbstractWebsite

The linear dynamics of rotating Rayleigh-Benard convection with rigid stress-free boundaries has been thoroughly investigated by Chandrasekhar (1961) who determined the marginal stability boundary and critical horizontal wavenumbers for the onset of convection and overstability as a function of the Taylor number T. No closed-form formulae appeared to exist and the results were tabulated numerically. However, by taking the Rayleigh number R as independent variable we have found remarkably simple expressions. When the Prandtl number P greater than or equal to P-c = 0.67659, the marginal stability boundary is described by the curve T(R) = R[(R/R-c)(1/2) - 1] where R-c = 27/4pi(4) is Rayleigh's famous critical value for the onset of stationary convection in a non-rotating system (T = 0). For P < P-c the marginal stability boundary is determined by this curve until it is intersected by the curve T(R, P) = R [(1+P/2(3) P-4)(1/2) (R/R-c)(1/2) - 1 + P/2P(2)]. A simple expression for the intersection point is derived and also for the critical horizontal wavenumbers for which, along the marginal stability boundary, instability sets in either as stationary convection or in an oscillatory fashion. A simple formula is derived for the frequency of the oscillations. Further, we have analytically determined critical points on the marginal stability boundary above which an increase of either viscosity or diffusivity is destabilizing. Finally, we show that if the fluid has zero viscosity the system is always unstable, in contradiction to Chandrasekhar's conclusion.

Kloosterziel, RC, Orlandi P, Carnevale GF.  2015.  Saturation of equatorial inertial instability. Journal of Fluid Mechanics. 767:562-594.   10.1017/jfm.2015.63   AbstractWebsite

Inertial instability in parallel shear flows and circular vorwes in a uniformly rotating system (f-plane) redistributes absolute linear momentum or absolute angular momentum in such a way as to neutralize the instability. In previous studies we showed that, in the absence of other instabilities, at high Reynolds numbers the final equilibrium can be predicted with a simple construction based on conservation of total momentum. In this paper we continue this line of research with a study of barotropic shear flows on the equatorial /3-plane, Through numerical simulations the evolution of the instability is studied in select illuminating cases: a westward flowing Gaussian jet With the flow axis exactly on the equator, a uniform shear flow and eastward and Wes t w ard flowing jets that have their flow axis shifted away from the equator. In the numerical simulations it is assumed that there are no along -stream variations. 'fins suppresses equatorial Rossby W a ve s and barotropic shear instabilities and allows only inertial instability to develop. We investigate whether for these flow S the equatorial t-plane the final equilibrated flow can be predicted as was possible for flows on the f-plane. For the Gaussian jet centred on the equator the prediction of the equilibrated flow is obvious by mere inspection of the initial momentum distribution and by assuming that momentum is mixed and homogenized to render the equilibrated flow inertially stable. For the uniform shear flow, however, due to the peculiar nature of the initial momentum distribution and the fact that the Coriolis parameter f varies with latitude, it appears that, unlike in our earlier studies of flows on the f-plane, additional constraints need to be considered to correctly predict the outcome of the highly nonlinear evolution of the instability, The mixing range of the linear shear flow and the value of the mixed momentum is determined numerically and this is used to predict the equilibrated flow that emerges from an eastward flowing jet that is shifted a small distance away from the equator. For shifts large enough to induce no shcar at the equator the equilibrium flow can be well predicted using the simple rccipe used in our carlicr studies of parallel shear flows on the f-plane. For thc westward flowing jet shifted a very small distance from the equator, no prcdiction appears feasible. For modcstly small shifts a prediction is possiblc by combining the empirical prcdiction for thc linear shear flow with a prediction similar to what we used in our previous studies for flows on the f-plane.

Kloosterziel, RC, Carnevale GF, Orlandi P.  2007.  Inertial instability in rotating and stratified fluids: barotropic vortices. Journal of Fluid Mechanics. 583:379-412.   10.1017/s0022112007006325   AbstractWebsite

The unfolding of inertial instability in intially barotropic vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated barotropic vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability drives an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process. It also shows that the equilibration process can result in anticyclones that are more susceptible to horizontal shear instabilities than they were initially, a phenomenon previously observed in laboratory and numerical studies.

Kloosterziel, RC, Carnevale GF.  2008.  Vertical scale selection in inertial instability. Journal of Fluid Mechanics. 594:249-269.   10.1017/s0022112007009007   AbstractWebsite

The linear instability of a barotropic flow with uniform horizontal shear in a stratified rotating fluid is investigated with respect to perturbations invariant in the alongflow direction. The flow can be inertially unstable if there is sufficiently strong anticyclonic shear, but only for sufficiently high Reynolds numbers Re. We determine the critical Reynolds numbers required for amplification of the instability as a function of Prandtl number, strength of the stratification and magnitude of the shear. The vertical scales at the onset of the instability are calculated. For Prandtl number P < 1.44 instability always sets in through stationary overturning motions, for P > 1.44 it may also commence through overstable (oscillatory) motions. For Re exceeding the critical value, we determine the vertical scale of the most rapidly amplifying modes and the corresponding growth rates and how they vary with Re, P, the shear and the strength of stratification.

Kloosterziel, RC, Orlandi P, Carnevale GF.  2007.  Saturation of inertial instability in rotating planar shear flows. Journal of Fluid Mechanics. 583:413-422.   10.1017/s0022112007006593   AbstractWebsite

Inertial instability in a rotating shear flow redistributes absolute linear momentum in such a way as to neutralize the instability. In the absence of other instabilities, the final equilibrium can be predicted by a simple construction based on conservation of total momentum. Numerical simulations, invariant in the along-stream direction, suppress barotropic instability and allow only inertial instability to develop. Such simulations, at high Reynolds numbers, are used to test the theoretical prediction. Four representative examples are given: a jet, a wall-bounded jet, a mixing layer and a wall-bounded shear layer.

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.

Frederiksen, JS, Carnevale GF.  1986.  Stability properties of exact nonzonal solutions for flow over topography. Geophysical and Astrophysical Fluid Dynamics. 35:173-207.   10.1080/03091928608245892   AbstractWebsite

The nonlinear stability properties of stationary exact nonzonal solutions for inviscid flow over topography are examined within a barotropic model in spherical geometry. For stationary solutions, such that the potential vorticity is proportional to the streamfunction, necessary and sufficient conditions for nonlinear stability are established. For a truncated system with rhomboidal truncation wave number J these are that the solid body rotation component of the zonal wind u(i) be negative, corresponding to westward flow, as J ->infinity. These results are established by using the methods of statistical mechanics. The sufficient condition for stability is also established by applying Arnol'd's method. The results are illustrated by numerical calculations. The stationary solutions are perturbed by disturbances in the streamfunction fields or by small changes in the topographic height; the climatic states for the system are obtained directly using statistical mechanics methods. The nonlinear stability properties of the stationary solutions are obtained by comparing the stationary solution with the climate, which for inviscid flow is shown to be unique. Stationary flows for which u(i) is eastward, are found to be unstable even in the limit as the streamfunction perturbation or change in the topographic height vanish. Large amplitude transient waves are generated which break the time invariance symmetry of the initial stationary flows. In contrast, for stationary flows with westward u(i), the climate is identical to the initial flow in the limit as the initial streamfuncton perturbation or the change in the topographic height vanishes. The linear instability characteristics of the stationary solutions are also obtained by solving a linear eigenvalue problem. The difficulties in establishing the stability properties of more general exact solutions, where the streamfunction is a general differentiable function of the potential vorticity, within numerical spectral models are discussed.

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.

Espa, S, Carnevale GF, Cenedese A, Mariani M.  2008.  Quasi-two-dimensional decaying turbulence subject to the effect. Journal of Turbulence. 9:1-18.   10.1080/14685240802464417   AbstractWebsite

Freely decaying quasi-2D turbulence under the influence of a meridional variation of the Coriolis parameter f ( effect) is experimentally and numerically modelled. The experimental flow is generated in a rotating electromagnetic cell where the variation of f is approximated by a nearly equivalent topographical effect. In the presence of a high effect, the initial disordered vorticity field evolves to form a weak polar anticyclonic circulation surrounded by a cyclonic zonal jet demonstrating the preferential transfer of energy towards zonal motions. In agreement with theoretical predictions, the energy spectrum becomes peaked near the Rhines wave number with a steep fall-off beyond, indicating the presence of a soft barrier to the energy transfer towards larger scales. DNS substantially confirmed the experimental observations.

Dietrich, D, Carnevale GF, Orlandi P.  2007.  Flow over the Mid Adriatic Pit. Nuovo Cimento Della Societa Italiana Di Fisica C-Geophysics and Space Physics. 30:277-290.   10.1393/ncc/i2007-10242-x   AbstractWebsite

The influence of the Mid Adriatic Pit (MAP) on the general circulation of the Adriatic is explored through numerical simulations. The numerical code used is the DieCAST model specifically modified for application to the Adriatic Sea. A ten-year simulation is performed and the ability of the model to capture important features of the Adriatic circulation is demonstrated. A series of numerical experiments on the importance of the MAP on the general circulation is performed. It is demonstrated that the current over the northern flank of the MAP, which flows from the Croatian toward the Italian coast, is primarily a topographic current and that such a current would reverse direction if the gradient of the bathymetry were reversed.