Decay laws, anisotropy and cyclone–anticyclone asymmetry in decaying rotating turbulence

Abstract

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.

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.…”

“…Moisy et al [25] have shown that flow fields originating from grid-generating decaying turbulence remain highly 3D, even at large rotation rates. Vertical velocity was not behaving as a passive scalar and its coupling with the large-scale flow was suggested to trigger shear instabilities.…”

Table-top rotating turbulence: an experimental insight through particle tracking

“…More recently, Baroud et al (2003) investigated turbulent water jets in a rotating annulus at Re λ = 360, and found the turbulent flow to be highly intermittent, independent of the Rossby number. Morize, Moisy, and Rabaud performed several experiments of decaying rotating turbulence in large and small facilities (Morize et al, 2005, Morize and Moisy, 2006, Moisy et al, 2010, and described in details some aspects of the coupling between the inertial wave pattern and the decaying turbulent field using high-resolution PIV. Accurate visualisations by means of reflective flakes of the formation and evolution of columnar eddies in rotating turbulence were performed by Davidson et al (2006).…”

The twists and turns of rotating turbulence

“…Skipping over many insightful contributions presented in the intervening 35 years, we turn to the study by Moisy et al (2010). Technology has moved on, allowing much F ocus luids on F more detailed measurements.…”

“…More surprisingly, the vertical correlation of the vertical velocity only grows a little faster than the horizontal correlation of the horizontal velocity, despite the suppression of ∂w/∂z. What Moisy et al (2010) suggest happens to the vertical velocity fluctuations is one of the major surprises.…”