Equipartition of energy and local isotropy in turbulent flows

Abstract

Homogeneous turbulence in which 〈v2〉 = 〈w 2〉 ≠ 〈u2〉 was produced experimentally, where 〈u2〉, 〈v2〉, and 〈w 2〉 are the mean-square turbulent velocities in x, y, and z direction, respectively. The decay of turbulence and the energy transfer between 〈u2〉 and (〈v2〉+〈w 2〉) were measured, and it was found that the larger components (〈v2〉 and 〈w2〉) are losing more energy due to viscosity than by transfer to the smaller component (〈u 2〉). However, 〈u2〉 is receiving enough energy by transfer to compensate for its decay and is in fact slowly increasing. The measurement of mean-square vorticity components shows that the turbulence is becoming locally isotropic at a faster rate than the equipartition of energy is taking place. In another set of experiments it was found that when approximately isotropic turbulence is subjected to deformation, the three components of turbulent energy become widely different in magnitude and that the turbulence is not locally isotropic. This indicates that even at high Reynolds number the deformation in a shear flow may cause anisotropy. The data on the turbulent shear flow near a solid wall confirm this conjecture. The connection of this investigation to turbulent flows in general is discussed. In particular, it follows that neither the turbulent energy nor the small-scale structure of turbulence rapidly settles down statistically to quasi-equilibrium. © 1957 The American Institute of Physics.