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

Harry L. Swinney

University of Texas at Austin

In three-dimensional (3D) turbulent flow, vortices stretch axially and

fold, but this process cannot occur in two dimensions. While all

turbulent flows are 3D on sufficiently small scales, atmospheric and

oceanic flows are approximately 2D on large scales. We study

turbulence in a rotating tank where the flow becomes 2D for

sufficiently rapid rotation rate (by the Taylor-Proudman theorem),

while for low rotation rates the flow is 3D [1]. We find that for 2D

turbulence the probability distribution function (PDF) for the

difference in velocity between two points is independent of the

separation r between the two points, i.e., the flow is self-similar.

In contrast, the PDFs for 3D turbulence are gaussian for large r and

exponential for small r. We further compare the 2D and 3D turbulence

flows by determing structure function scaling exponents and by

applying the beta and gamma tests of the hierarchical structure model;

these quantities will be defined and discussed. The conclusion is that

2D turbulence in a rotating flow is surprisingly intermittent, but the

intermittency is a consequence of large coherent vortices rather than

the stretching and folding of vortex lines as in 3D.

*Supported by ONR

[1] C.N. Baroud, B.P. Plapp, Z.S. She, and H. L. Swinney, submitted