EXTENSION OF THE KOLMOGOROV REFINED SIMILARITY HYPOTHESIS FOR ISOTROPIC TURBULENCE

The refined similarity hypothesis proposed by Kolmogorov in 1962 to ex plain the intermittent structure of isotropic turbulence is modified. It is shown that a slight but fundamental deviation from the hypothesi s leads to success in precisely bridging between the statistics of lon gitudinal velocity increment across distance r and that of energy diss ipation rate averaged over a domain of scale r in a wide range of r re aching the dissipation range, when one assumes a binomial Canter set m odel for the latter statistics. The success also covers a reasonable p rediction of the statistics of longitudinal velocity gradient with pro per skewness and kurtosis for any large Reynolds number based on the T aylor microscale.