Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows

We have made velocity time series measurements ~using hot film probes! and velocity field measurements ~using particle image velocimetry! on turbulent flow in a rotating annulus. For low annulus rotation rates the Rossby number was of order unity and the flow was three-dimensional ~3D!, but at high rotation rates the Rossby number was only about 0.1, comparable to the value for oceans and the atmosphere on large length scales. The low Rossby number ~quasi-geostrophic! flow was nearly two-dimensional ~2D!, as expected from the Taylor–Proudman theorem. For the 3D flow we found that the probability distribution function ~PDF! for velocity differences along the direction of the flow, dv(d)5v(x01d)2v(x0), was Gaussian for large separations d and non-Gaussian ~with exponential tails! for small d, as has been found for nonrotating turbulent flows. However, for low Rossby number flow, the PDF was self-similar ~independent of d! and non-Gaussian. The exponents characterizing the structure functions, Sp5^(dv) &;dp were obtained by the extended self-similarity method. For 3D flow the exponents departed from p/3 with increasing p, as has been found for turbulence in nonrotating flows, while for the quasi-2D turbulent flow, the exponents increased linearly with p, as expected for a self-similar flow. We applied the b-test of the hierarchical structure model @She and Lévêque, Phys. Rev. Lett. 72, 336 ~1994!# and found that b remained constant at b.0.75 as the rotation was increased from the 3D to the 2D regime; this indicates that both the quasi-2D and 3D flows are highly intermittent. The PIV images provided another indication of the intermittency—both the quasi-2D and 3D flows had coherent vortices which could be distinguished from the background flow. We also applied the g-test of the hierarchical structure model and found that g increased from 0.18 for the 3D flow to 0.34 for the quasi-2D flow; the latter value is in accord with expectation for self-similar turbulence. We conclude that our rotating 3D flow is similar to nonrotating turbulent flows, while the rotating quasi-2D turbulence is different from both the 3D rotating turbulence and from nonrotating 2D turbulence studied in other experiments. © 2003 American Institute of Physics. @DOI: 10.1063/1.1577120#