EVIDENCE AGAINST THE KOLMOGOROV REFINED SIMILARITY HYPOTHESIS

It is found that the well-known "refined similarity hypothesis," proposed by Kolmogorov and Obukhov in 1962, fails in a typical direct numerical simulation of three-dimensional turbulence: If r is an inertial-range scale, the velocity difference across a domain of linear dimension r is almost statistically independent of the average dissipation within the domain. This result casts doubt on the often-used relation, zeta(p) = p/3 - mu(p/3), between scaling indices zeta(p) for velocity structure functions and scaling indices mu(q) for moments of locally averaged dissipation. It seems questionable that a single turbulence model can predict both sets of exponents successfully. Other aspects of the treatment of intermittency in isotropic turbulence may also need reconsideration.