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

Published online by Cambridge University Press:  12 October 2010

F. MOISY ,
C. MORIZE ,
M. RABAUD  and
J. SOMMERIA
F. MOISY*
Affiliation:
Laboratoire FAST, Université Paris-Sud 11, Université Pierre et Marie Curie, CNRS, Bâtiment 502, F-91405 Orsay Cedex, France
C. MORIZE
Affiliation:
Laboratoire FAST, Université Paris-Sud 11, Université Pierre et Marie Curie, CNRS, Bâtiment 502, F-91405 Orsay Cedex, France
M. RABAUD
Affiliation:
Laboratoire FAST, Université Paris-Sud 11, Université Pierre et Marie Curie, CNRS, Bâtiment 502, F-91405 Orsay Cedex, France
J. SOMMERIA
Affiliation:
Coriolis/LEGI, 21 avenue des Martyrs, F-38000 Grenoble, France
*
†Email address for correspondence: [email protected]
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Abstract

The effect of a background rotation on the decay of grid-generated turbulence is investigated from experiments using the large-scale ‘Coriolis’ rotating platform. A first transition occurs at 0.4 tank rotation (instantaneous Rossby number Ro ≃ 0.25), characterized by a t−6/5 → t−3/5 transition of the energy-decay law. After this transition, anisotropy develops in the form of vertical layers, where the initial vertical velocity fluctuations remain trapped. The vertical vorticity field develops a cyclone–anticyclone asymmetry, reproducing the growth law of the vorticity skewness, Sω(t) ≃ (Ωt)0.7, reported by Morize, Moisy & Rabaud (Phys. Fluids, vol. 17 (9), 2005, 095105). A second transition is observed at larger time, characterized by a return to vorticity symmetry. In this regime, the layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, and eventually become unstable. The present results indicate that the shear instability of the vertical layers contributes significantly to the re-symmetrization 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 nature of the initial conditions in the decay of rotating turbulence.

JFM classification

Geophysical and Geological Flows: Rotating flows Turbulent Flows: Rotating turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 5 - 35
Copyright
Copyright © Cambridge University Press 2010

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References

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Moisy supplementary material

Movie 1. Experimental setup, seen from the rotating frame. The first sequence shows the water channel, 4 m wide, 9 m long and 1 m thickness, mounted on the 13-m-diameter rotating platform. The second sequence shows the grid, translated at constant velocity Vg = 0.3 m/s along the channel (Reynolds number Reg = 42 000). The horizontal green line on the grid marks the intersection with the laser sheet, used for the Particule Image Velocimetry (PIV) measurements in the horizontal plane. The free surface disturbances in the wake of the grid are essentially damped when PIV measurements are performed.

Download Moisy supplementary material(Video)
Video 9.6 MB

Moisy supplementary material

Movie 1. Experimental setup, seen from the rotating frame. The first sequence shows the water channel, 4 m wide, 9 m long and 1 m thickness, mounted on the 13-m-diameter rotating platform. The second sequence shows the grid, translated at constant velocity Vg = 0.3 m/s along the channel (Reynolds number Reg = 42 000). The horizontal green line on the grid marks the intersection with the laser sheet, used for the Particule Image Velocimetry (PIV) measurements in the horizontal plane. The free surface disturbances in the wake of the grid are essentially damped when PIV measurements are performed.

Download Moisy supplementary material(Video)
Video 3.5 MB

Moisy supplementary material

Movie 3. Spanwise vorticity ωy measured in the vertical plane (x,z), for a rotation rate Ω = 0.20 rad/s (T = 30 s), showing the growth of anisotropy and the gradual formation of vertical layers. The grid is translated from left to right, and crosses the center of the imaged area at t = 0. The sampling rate is not constant: the delay between two images is increased in 4 steps, from 2 s to 20 s. Due to the horizontal flow induced by the inertial wave, the structures quickly enter and leave the vertical plane.

Download Moisy supplementary material(Video)
Video 14.5 MB

Moisy supplementary material

Movie 3. Spanwise vorticity ωy measured in the vertical plane (x,z), for a rotation rate Ω = 0.20 rad/s (T = 30 s), showing the growth of anisotropy and the gradual formation of vertical layers. The grid is translated from left to right, and crosses the center of the imaged area at t = 0. The sampling rate is not constant: the delay between two images is increased in 4 steps, from 2 s to 20 s. Due to the horizontal flow induced by the inertial wave, the structures quickly enter and leave the vertical plane.

Download Moisy supplementary material(Video)
Video 8.5 MB

Moisy supplementary material

Movie 2. Vertical vorticity ωz measured in an horizontal plane (y,x) at mid-height, for a rotation rate of Ω = 0.20 rad/s (T = 30 s). The background rotation is anticlockwise. Positive vorticity (in red) is cyclonic, and negative vorticity (in blue) is anticyclonic. The sampling rate is not constant: the delay between two images is increased in 4 steps, from 2 s to 20 s. At small time a strong inertial wave (anticyclonic circular translation, of period T / 2 = 15 s) advects the turbulent flow. At intermediate time (t ≈ 400 s), well defined cyclonic vortices emerge. Note the pairing event at t ≈ 1000 s. At large time, t ≈ 3000 s, the vorticity field is dominated by small scale symmetric fluctuations advected by the large scale horizontal motion

Download Moisy supplementary material(Video)
Video 12.4 MB

Moisy supplementary material

Movie 2. Vertical vorticity ωz measured in an horizontal plane (y,x) at mid-height, for a rotation rate of Ω = 0.20 rad/s (T = 30 s). The background rotation is anticlockwise. Positive vorticity (in red) is cyclonic, and negative vorticity (in blue) is anticyclonic. The sampling rate is not constant: the delay between two images is increased in 4 steps, from 2 s to 20 s. At small time a strong inertial wave (anticyclonic circular translation, of period T / 2 = 15 s) advects the turbulent flow. At intermediate time (t ≈ 400 s), well defined cyclonic vortices emerge. Note the pairing event at t ≈ 1000 s. At large time, t ≈ 3000 s, the vorticity field is dominated by small scale symmetric fluctuations advected by the large scale horizontal motion

Download Moisy supplementary material(Video)
Video 7.8 MB