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