Anisotropy and coherent vortex structures in planetary turbulence

Physics of Fluids, 1996

Journal of Fluid …, 1993

Journal of Physical Oceanography, 2011

Large-scale vortices, that is, eddies whose characteristic length scale is larger than the local Rossby radius of deformation R d , are ubiquitous in the oceans, with anticyclonic vortices more prevalent than cyclonic ones. Stability or robustness properties of already formed shallow-water vortices have been investigated to explain this cyclone-anticyclone asymmetry. Here the focus is on possible asymmetries during the generation of vortices through barotropic instability of a parallel flow. The initial stage and the nonlinear stage of the instability are studied by means of linear stability analysis and direct numerical simulations of the one-layer rotating shallow-water equations, respectively. A wide variety of parallel flows are studied: isolated shears, the Bickley jet, and a family of wakes obtained by combining two shears of opposite signs.

Astronomy & Astrophysics, 2007

We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow. We make use of high-resolution global two-dimensional compressible hydrodynamic simulations. We introduce the concept of nonlinear adjustment to describe the transition of unbalanced vortical fields to a long-lived configuration. We discuss the conditions under which vortical perturbations evolve into long-lived persistent structures and we describe the properties of these equilibrium vortices. The properties of equilibrium vortices appear to be independent from the initial conditions and depend only on the local disk parameters. In particular we find that the ratio of the vortex size to the local disk scale height increases with the decrease of the sound speed, reaching values well above the unity. The process of spiral density wave generation by the vortex, discussed in our previous work, appear to maintain its efficiency also at nonlinear amplitudes and we observe the formation of spiral shocks attached to the vortex. The shocks may have important consequences on the long term vortex evolution and possibly on the global disk dynamics. Our study strengthens the arguments in favor of anticyclonic vortices as the candidates for the promotion of planetary formation. Hydrodynamic shocks that are an intrinsic property of persistent vortices in compressible Keplerian flows are an important contributor to the overall balance. These shocks support vortices against viscous dissipation by generating local potential vorticity and should be responsible for the eventual fate of the persistent anticyclonic vortices. Numerical codes have be able to resolve shock waves to describe the vortex dynamics correctly.

Physical Review E, 2014

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024 3 grid points and Reynolds numbers of ≈1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the kinetic energy displays a perpendicular (horizontal) spectrum with power-law behavior compatible with ∼k −5/3 ⊥ , including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

arXiv (Cornell University), 2009

The effect of a background rotation on the decay of homogeneous turbulence produced by a grid is experimentally investigated. Experiments have been performed in a channel mounted in the large-scale 'Coriolis' rotating platform, and measurements have been carried out in the planes normal and parallel to the rotation axis using particle image velocimetry. After a short period of about 0.4 tank rotation where the energy decays as t −6/5 , as in classical isotropic turbulence, the energy follows a shallower decay law compatible with t −3/5 , as dimensionally expected for energy transfers governed by the linear timescale Ω −1. The crossover occurs at a Rossby number Ro ≃ 0.25, without noticeable dependence with the grid Rossby number. After this transition, anisotropy develops in the form of vertical layers where the initial vertical velocity remains trapped. These layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, producing significant horizontal gradient of vertical velocity which eventually become unstable. After the Ro ≃ 0.25 transition, the vertical vorticity field first develops a cyclone-anticyclone asymmetry, reproducing the growth law of the vorticity skewness, S ω (t) ≃ (Ωt) 0.7 , reported by Morize, Moisy & Rabaud [Phys. Fluids 17 (9), 095105 (2005)]. At larger time, however, the vorticity skewness decreases and eventually returns to zero. The present results indicate that the shear instability of the vertical layers contribute significantly to the re-symmetrisation of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the initial conditions in the decay of rotating turbulence.

Physics of Fluids, 1998

2019

We present a numerical model that reveals a mechanism governing the polar atmospheric dynamics of Jupiter, Saturn, Uranus and Neptune. Exploration of the polar regions of the gas giants has produced surprisingly diverse results, with Cassini finding a single, intense, compact polar cyclone precisely centered on each pole of Saturn, and Voyager data and ground-based observations suggesting Uranus and Neptune have dominant, single polar cyclones as well. The Juno spacecraft at Jupiter finds several tightly packed cyclones surrounding a central cyclone offset from the poles. These discoveries raise questions about the mechanism that differentiates these polar atmospheric dynamics regimes. To help determine what physical mechanisms control these differences, we use the Explicit Planetary Isentropic Coordinate (EPIC) model to carry out forced-turbulence shallow-water simulations in a gamma-plane configuration, i.e. a Cartesian grid with a pole placed at the center. The model is forced by small-scale stochastic mass pulses that parametrically represent cumulus storms. The effects of three parameters, the planetary Burger number, Bu = (Ld / a) 2 (Ld is the Rossby deformation radius, a is the planetary radius), input storm strength, s, and proportion of cyclonic and anticyclonic storms injected into the domain, α, are systematically investigated. Bu emerges to be the most important, able to distinguish between four distinct dynamical regimes, matching those of the giant planets, which from large to small Bu, are: i) a large cyclonic polar vortex (i.e., Uranus/Neptune-like), ii) a compact intense cyclonic polar vortex (Saturn-like), iii) two large vortices or one vortex offset from the pole (transitional), and iv) meandering jets with no centrally dominant vortex, or with multiple circumpolar cyclones (Jupiter-like). The boundaries of these regimes are found to be only slightly modulated by the values of s and α. By applying this correlation with respect to Bu in reverse, an observation of a particular polar regime could in principle be used to constrain Ld .

Physics of Fluids, 2001

The anisotropic characteristics of small-scale forced 2D turbulence on the surface of a rotating sphere are investigated. In the absence of rotation, the Kolmogorov k Ϫ5/3 spectrum is recovered with the Kolmogorov constant C K Ϸ6, close to previous estimates in plane geometry. Under strong rotation, in long-term simulations without a large-scale drag, a Ϫ5 slope emerges in the vicinity of the zonal axis (k x →0), while a Ϫ5/3 slope prevails in other sectors far away from the zonal axis in the wave number plane. This picture is consistent with the new flow regime recently simulated by Chekhlov et al. ͓Physica D 98, 321-334 ͑1995͔͒ and Smith and Waleffe ͓Phys. Fluids 11, 1608-1622 ͑1999͔͒ on the beta plane. The concentration of energy in the zonal components and breaking of isotropy are caused by the strongly anisotropic spectral energy transfer and the stabilization of zonal mean flow by the meridional gradient of the planetary vorticity. The sharp tilt-up of the spectrum along the zonal axis was qualitatively understood through the scale-dependent stability property of the zonal flow. Under planetary rotation, the capacity for the zonal jets to hold energy and remain stable sharply increases with an increase of the meridional scale of the jets. In our simulations that were virtually inviscid at the large scales, the energy spectrum along the zonal axis tilts up all the way to the largest possible scale, indicating an apparent up-scale energy ''cascade'' along the zonal axis. This apparent up-scale cascade corresponds to a process of continuous mergers of zonal jets that does not cease until reaching the largest scale. This picture is consistent with the inviscid scenario for jet merging discussed by Manfroi and Young ͓J. Atmos. Sci. 56, 784-800 ͑1999͔͒. It contrasts the viscous scenario ͑for flows under the influence of a constant bottom drag͒ simulated in several previous studies, in which a distinct and finite jet scale emerges asymptotically.

Physics of Fluids

The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two-dimensional (2D) columnar vortices and three-dimensional (3D) inertial waves, whose relative energies depend on the precession parameter Po. The vortices resemble the typical condensates of geostrophic turbulence, are aligned along the rotation axis (with zero wavenumber in this direction, kz = 0), and are fed by the 3D waves through nonlinear transfer of energy, while the waves (with kz≠0) in turn are directly fed by the precessional instability of the background flow. The vortices themselves undergo inverse cascade of energy and exh...

Journal of Fluid Mechanics, 2013

We study fluid-particle motion in the velocity field induced by a quasi-stationary point vortex structure consisting of one upper-layer vortex and two identical vortices in the bottom layer of a rotating two-layer fluid. The regular regimes are investigated, and the possibility of chaotic regimes (chaotic advection) under the effect of quite small non-stationary disturbances of stationary configurations has been shown. Examples of different scenarios are given for the origin and development of chaos. We analyse the role played by the stochastic layer in the processes of mixing and in the capture of fluid particles within a vortex area. We also study the influence of stratification on these effects. It is shown that regular and chaotic advection situations exhibit significant differences in the two layers.

Journal of Fluid Mechanics, 1994

Numerical simulations investigating the formation and stability of quasi-two-dimensional coherent vortices in rotating homogeneous three-dimensional flow are described. In a numerical study of shear flows Lesieur, Yanase & Métais (1991) found that cyclones (respectively anticyclones) with |ω2D| ∼O(2Ω), where ω2Dis the vorticity and Ω is the rotation rate, are stabilized (respectively destabilized) by the rotation. A study of triply periodic pseudo-spectral simulations (643) was undertaken in order to investigate the vorticity asymmetry in homogeneous turbulence. Specifically, we examine (i) the possible three-dimensionalization of initially two-dimensional vortices and (ii) the emergence of quasi-two-dimensional structures in initially-isotropic three-dimensional turbulence. Direct numerical simulations of the Navier—Stokes equations are compared with large-eddy simulations employing a subgridscale model based on the second-order velocity structure function evaluated at the grid sep...

Physical Review Letters, 2013

The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient and Coriolis and buoyancy forces. This leads to a quasigeostrophic balance in which, in a two-dimensional-like fashion, the energy injected by solar radiation, winds, or tides goes to large scales in what is known as an inverse cascade. Yet, except for Ekman friction, energy dissipation and turbulent mixing occur at a small scale implying the formation of such scales associated with breaking of geostrophic dynamics through wave-eddy interactions or frontogenesis, in opposition to the inverse cascade. Can it be both at the same time? We exemplify here this dual behavior of energy with the help of three-dimensional direct numerical simulations of rotating stratified Boussinesq turbulence. We show that efficient small-scale mixing and large-scale coherence develop simultaneously in such geophysical and astrophysical flows, both with constant flux as required by theoretical arguments, thereby clearly resolving the aforementioned contradiction.

Fluids, 2016

The key element of Geophysical Fluid Dynamics-reorganization of potential vorticity (PV) by nonlinear processes-is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies.

Physical Review E, 2013

We perform numerical simulations of decaying rotating stratified turbulence and show, in the Boussinesq framework, that helicity (velocity-vorticity correlation), as observed in super-cell storms and hurricanes, is spontaneously created due to an interplay between buoyancy and rotation common to large-scale atmospheric and oceanic flows. Helicity emerges from the joint action of eddies and of inertia-gravity waves (with inertia and gravity with respective associated frequencies f and N ), and it occurs when the waves are sufficiently strong. For N/f < 3 the amount of helicity produced is correctly predicted by a quasi-linear balance equation. Outside this regime, and up to the highest Reynolds number obtained in this study, namely Re ≈ 10000, helicity production is found to be persistent for N/f as large as ≈ 17, and for ReF r 2 and ReRo 2 respectively as large as ≈ 100 and ≈ 24000.