Cyclone-anticyclone asymmetry and alignment statistics in homogeneous rotating turbulence

Abstract

International audienceThe cyclone-anticyclone asymmetry occurring in rotating turbulence is investigated through the analysis of the alignment statistics between vorticity and the rotation vector. The advantage of this approach, as compared to the usual measurement of the vertical vorticity skewness, is that the symmetry-breaking can be thus quantified through the analysis of first- and second-order moments, whose statistics convergence is more easily achieved than that of third-order ones. The vorticity/rotation alignment statistics are investigated by direct numerical simulation, both in forced and in freely decaying homogeneous turbulence. In the forced case, the cyclone-anticyclone asymmetry gets stronger as the Rossby number is decreased, whereas the opposite behavior occurs in the decaying case. These findings are shown to be consistent with the existence of a non-monotonic Rossby-number dependence of the asymmetry. A preferential antialignment of vorticity with the rotation vector is found in all the flows considered, a behavior supported by geometrical arguments and by a Taylor expansion of the Navier-Stokes equations for early times of rotation and in the weak rotation limit. A multiscale analysis of the alignment properties between vorticity and the rotation vector is also carried out in the forced case, evidencing the existence of a scale at which both the symmetry-breaking and the collinearity between the two vectors are maxima

Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows

“…Such cyclone-anticyclone asymmetry is observed in experimental and numerical studies at moderately low values of the Rossby number (Bartello at al. 1994;Bourouiba & Bartello 2007;Smith & Waleffe 1999;Morize et al 2005;Sreenivasan & Davidson 2008;Moisy et al 2011;Deusebio et al 2014;Naso 2015). Does cyclone-anticyclone asymmetry persist for very low Rossby number, or is it a finite-Rossby-number effect?…”

Multiscale analysis of the structure of homogeneous rotating turbulence

“…The integral scale of the resulting flows is such that r f /L ∈ [1.2, 1.7], where r f = 2π/1.5 is the threshold between the truncated Euler system and the Navier-Stokes regime. This forcing method was already used to investigate homogeneous rotating turbulence [35,37,42] and allows one to reach a statistically steady state after a few eddy turnover times starting from a random incompressible velocity field.…”

“…In this latter run, rotation effects are therefore expected to be dominant over inertial ones at all scales. Typical instantaneous densities of vorticity magnitude in a horizontal plane are displayed in As already mentioned, we used sets of fluid elements equally spaced to reconstruct the perceived velocity gradient tensor, a procedure already used in HIT [10,12,13] and in homogeneous rotating turbulence [35,37]. For each value of the Rossby number, several values of r 0 ranging from less than or approximately η to approximately L/ √ 2 were used so as to cover the entire inertial range.…”

“…Since rotating flows have a preferential direction along the axis of rotation, it is first natural to investigate the orientation between this axis and the vectors characterizing the flow geometry: vorticity, vortex stretching vector, and strain eigenframe. The statistics of alignment between the rotation vector rot and perceived vorticity (r 0 ) in homogeneous rotating turbulence were investigated by direct numerical simulation in [37]. Both vectors were found to be preferentially antialigned at any scale, a property related to the cyclone-anticyclone asymmetry.…”

“…The Eulerian statistics of M conditioned on the topology of rotating turbulence were investigated in [35]. Similar measurements of the alignment statistics between vorticity and the rotation vector, related to the cyclone-anticyclone asymmetry arising in rotating turbulence [18,19,36], were then presented in [37].…”