A NOTE ON KOLMOGOROVS 3RD-ORDER STRUCTURE-FUNCTION LAW, THE LOCAL ISOTROPY HYPOTHESIS AND THE PRESSURE-VELOCITY CORRELATION

We show that Kolmogorov's (1941b) inertial-range law for the third-ord er structure function can be derived from a dynamical equation includi ng pressure terms and mean flow gradient terms. A new inertial-range l aw, relating the two-point pressure-velocity correlation to the single -point pressure-strain tensor, is also derived. This law shows that th e two-point pressure-velocity correlation, just like the third-order s tructure function, grows linearly with the separation distance in the inertial range. The physical meaning of both this law and Kolmogorov's law is illustrated by a Fourier analysis. An inertial-range law is al so derived for the third-order velocity-enstrophy structure function o f two-dimensional turbulence. It is suggested that the second-order vo rticity structure function of two-dimensional turbulence is constant a nd scales with epsilon(omega)(2/3) in the enstrophy inertial range, ep silon(omega) being the enstrophy dissipation. Owing to the constancy o f this law, it does not imply a Fourier-space inertial-range law, and therefore it is not equivalent to the k(-1) law for the enstrophy spec trum, suggested by Kraichnan (1967) and Batchelor (1969).