Possible Departures from Local Isotropy in the Small Scale Structure of Turbulent Velocity Fields

摘要

Two weakened similarity hypotheses are proposed as possible replacements for the two Kolmogorov similarity hypotheses as descriptions of laboratory turbulence. It is shown that these hypotheses yield consequences which are in full agreement with the whole range of laboratory, atmospheric, and oceanic measurements bearing on the question of the existence of local isotropy in turbulent flows. However, the weakened hypotheses are fully consistent with the non-existence of local isotropy. It is concluded that a new class of measurements - the measurement of cross-stream variations in the velocity correlations - would be required to establish the existence or non-existence of local isotropy. One consequence of the proposed weakened similarity hypotheses is that the Kolmogorov constant C is not a constant, but is, instead, a flow-dependent quantity, depending on velocity gradients. This is in at least qualitative agreement with the large scatter in values of C reported in the literature. (ERA citation 05:021035)