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02/27/04 Colloquium
SUSAN KURIEN
CENTER FOR NONLINEAR STUDIES/THEORETICAL DIVISION
LOS ALAMOS NATIONAL LABORATORY
CENTER FOR NONLINEAR STUDIES/THEORETICAL DIVISION
LOS ALAMOS NATIONAL LABORATORY
Symmetry Breaking in Turbulent Flow Statistics--Rotation and Reflection
Abstract: A question of interest in studying turbulent velocity statistics is whether or not such statistics are spatially isotropic. The benchmark work of Kolomogov (1941) postulated that there exists a range of scales much smaller than the (anisotropic) large scales within which turbulence recovers isotropy. This is the "local isotropy" assumption of Kolmogorov and lead to the derivation of exact results for third-order velocity statistics.Since most turbulent flows are apparently anisotropic in the large scales we would like to quantify the degree to which the rotational symmetry-breaking penetrates into the small scales and better understand the local isotropy assumption. To do this we use SO(3) group decomposition methods to disentangle various anisotropic contributions which contaminate the isotropic scaling expected from a Kolmogorov-type argument. We show that, for the type of statistics usually studied, the small-scales in turbulence are not strictly isotropic but rather display a hierarchy of scaling exponents with the leading exponent coming from the isotropic contribution.
There is another symmetry-breaking which can occur in isotropic flows due to the presence of helicity - - the breaking of reflection-symmetry. I will show new results which predict the scaling behavior due to the breaking of reflection-symmetry in the velocity field; this result yields the counterpart to the Kolmogorov result for reflection-symmetric flows. Experimental and numerical results from various sources will be presented where appropriate.
