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, ζp = p/3 − μp/3, between scaling indices ζp for velocity structure functions and scaling indices μq 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.