# Observations on Rapidly Rotating Turbulence

## Abstract

Experiments on rapidly rotating turbulence have been reported in recent years in which the Rossby number, *Ro*, drifts down towards unity as the energy of the turbulence decays (Davidson et al., 2006; Staplehurst et al., 2008). The experiments were performed in a large vessel, approximately 35 integral scales in each direction. Moreover, any mean flow was carefully suppressed and so the resulting motion constitutes a good approximation to homogeneous turbulence. In line with other experiments, and certain numerical simulations, four robust phenomena were observed: (i) when *Ro* reaches a value close to unity, columnar eddies start to form and these eventually dominate the large, energy-containing scales; (ii) during the formation of these columnar eddies, the integral scale parallel to the rotation axis grows linearly with time; (iii) more cyclones than anticyclones are observed; and (iv) the rate of energy decay is reduced by rotation. The experiments also show that, despite the fact that *Ro*∼1, the columnar eddies form through simple linear wave propagation, in which inertial waves pump energy along the rotation axis. In this paper we explain: (i) why columnar vortices form in such experiments; (ii) why linear behaviour dominates the dynamics in (Staplehurst et al., 2008), even though *Ro*∼1; and (iii) why cyclones are more frequently observed than anticyclones. We also re-examine the energy decay data in (Staplehurst et al., 2008) and show that, to a reasonable approximation, it takes the form *u* ^{2}∼(Ω*t*)^{−1}. We offer one possible explanation for this behaviour.

## Keywords

Rotation Axis Columnar Structure Integral Scale Energy Decay Vortex Sheet## Preview

Unable to display preview. Download preview PDF.

## References

- [1]Davidson, P.A., Staplehurst, P.J. & Dalziel S.B., 2006, On the evolution of eddies in a rapidly rotating system.
*J Fluid Mech.***557**, 135-144. CrossRefGoogle Scholar - [2]Staplehurst P.J., Davidson P.A. & Dalziel S.B., 2008, Structure formation in homogeneous freely decaying rotating turbulence.
*J. Fluid Mech.***598**, 81-105. CrossRefGoogle Scholar - [3]Hopfinger, E.J., Browand, F.K. & Gagne, Y., 1982, Turbulence and waves in a rotating tank.
*J. Fluid Mech.***125**, 505-534. CrossRefGoogle Scholar - [4]Morize, C., Moisy, F. & Rabaud, M., 2005, Decaying grid-generated turbulence in a rotating tank.
*Phys. Fluids***17**, 095105. CrossRefGoogle Scholar - [5]Morize, C. & Moisy, F., 2006, Energy decay of rotating turbulence with confinement effects.
*Phys. Fluids***18**, 065107. CrossRefGoogle Scholar - [6]Waleffe, F., 1993, Inertial transfers in the helical decomposition.
*Phys. Fluids A***5**(3), 667-685. CrossRefGoogle Scholar - [7]Smith, L.M. & Waleffe, F., 1999, Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence.
*Phys. Fluids***11**(6), 1608-1622. CrossRefGoogle Scholar - [8]Smith, L.M. & Lee, Y., 2005, On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number.
*J. Fluid Mech.***535**, 111-142. CrossRefGoogle Scholar - [9]Cambon, C., Mansour, N.N. & Godeferd, F.S., 1997, Energy transfer in rotating turbulence.
*J. Fluid Mech.***337**, 303-332. CrossRefGoogle Scholar - [10]Sreenivasan, B. & Davidson, P.A., 2008, On the formation of cyclones and anticyclones in a rotating fluid.
*Phys. Fluids***20**(8), 085104. CrossRefGoogle Scholar - [11]Davidson, P.A., Sreenivasan, B. & Aspden, A.J., 2007, Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field.
*Phys. Rev. E***75**, 026304. CrossRefGoogle Scholar - [12]Gence, J.-N. & Frick C., 2001, Naissance des correlations triple de vorticite dans une turbulence homogene soumise a une rotation.
*C. R. Acad. Sc. Paris, Ser. IIB***329**, 351-362. Google Scholar - [13]Davidson, P.A., 2004, Turbulence, an introduction for scientists and engineers,
*Oxford University Press*. Google Scholar