Coherent structures in rotating three-dimensional turbulence

Abstract

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 ω2D is 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 separation and with simulations employing hyperviscosity.Isolated coherent two-dimensional vortices, obtained from a two-dimensional decay simulation, were superposed with a low-amplitude three-dimensional perturbation, and used to initialize the first set of simulations. With Ω = 0, a three-dimensionalization of all vortices was observed. This occurred first in the small scales in conjunction with the formation of longitudinal hairpin vortices with vorticity perpendicular to that of the initial quasi-two-dimensional flow. In agreement with centrifugal stability arguments, when 2Ω = [ω2D]rms a rapid destabilization of anticyclones was observed to occur, whereas the initial two-dimensional cyclonic vortices persisted throughout the simulation. At larger Ω, both cyclones and anticyclones remained two-dimensional, consistent with the Taylor—Proudman theorem. A second set of simulations starting from isotropic three-dimensional fields was initialized by allowing a random velocity field to evolve (Ω = 0) until maximum energy dissipation. When the simulations were continued with 2Ω = [ω · Ω]rms/Ω, the three-dimensional flow was observed to organize into two-dimensional cyclonic vortices. At larger Ω, two-dimensional anticyclones also emerged from the initially-isotropic flow. The consequences for a variety of industrial and geophysical applications are clear. For quasi-two-dimensional eddies whose characteristic circulation times are of the order ofder of Ω−1, rotation induces a complete disruption of anticyclonic vortices, while stabilizing cyclonic ones.

Experiments on rapidly rotating turbulent flows

“…The rotating turbulence is still homogeneous ͑within the horizontal plane͒ but no longer 3C isotropic. Instead, based on the invariant maps one tends to classify the rotating turbulence as a 3D2C flow, consistent with other numerical simulations 22 Figure 12 shows the time-averaged temporal velocity correlation coefficients ͗ ii ͘ TA and ͗ ␣␣ ͘ TA ͑with ␣ = 1 and 3͒ for ͕H , ⍀ , I͖ = ͕50,1,4͖, ͕50,5,4͖, and ͕50,10,4͖. The correlation time is now scaled by the rotational time scale T ⍀ instead of the eddy turn-over time scale T e .…”

“…Numerical simulations have shown that the faster growth of certain integral length scales is also related to the inhibited energy cascade. [21][22][23] Among the most recent experimental studies are those by Baroud et al, 13,14 Morize and co-workers, 15,24 and by Davidson an co-workers. 16, 17 Baroud and co-workers studied the flow in a rotating annulus with forcing created by pumping water into ͑out of͒ the annulus through an inner ͑outer͒ ring of holes on the bottom of the annulus.…”

Dimensional transition in rotating turbulence

“…The breaking of asymmetry between cyclonic and anticyclonic vortices, which has been observed both in experiments [15,25,[28][29][30] and in numerical simulations [20,31,32], is a distinctive feature of rotating turbulent flows. Here we are interested to investigate how this asymmetry is influenced both by the rotation and the confinement of the flow.…”

“…Several explanations have been proposed to explain this phenomenon. In particular, it has been shown that the cyclones and anticyclones have different stability properties [31] and different probabilities to be generated at finite Rossby number [33]. Moreover, the correlations between the strain tensor and the vorticity in isotropic turbulence can be responsible for the development of a positive skewness of vertical vorticity when the flow is suddenly subjected to rotation [34].…”

Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence

“…The Coriolis term breaks the parity invariance of the governing equation of the flow, and introduces a scale-independent time scale which induces two-dimensionalization at larger scales more effectively. Therefore, the Coriolis effect originates cyclone-anticyclone asymmetry with enhanced stretching of cyclonic vorticity and destabilization of anticyclonic one due to the centrifugal instability and the vortex tilting [4].To classify the flow properties in rotating systems, the Rossby number Ro, which is the ratio between the linear and nonlinear time scales, has been used [5]. Note that though various definitions of Ro are used in literature, the following facts are independent of its detailed definition.…”