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∼(Ωt)−1. We offer one possible explanation for this behaviour.