EXAMINATION OF HYPOTHESES IN THE KOLMOGOROV REFINED TURBULENCE THEORYTHROUGH HIGH-RESOLUTION SIMULATIONS .1. VELOCITY-FIELD

The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbu lence theory (K62) are examined directly and quantitatively by using h igh-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 512(3) resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 256(3) large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynami cs. The Kolmogorov constant for the k(-5/3) energy spectrum obtained f rom the 512(3) DNS flow is 1.68 +/- 0.15. The probability distribution of the locally averaged disspation rate epsilon(r) over a length scal e r is nearly log-normal in the inertial subrange, but significant dep artures are observed for high-order moments. The intermittency paramet er mu, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0. 28. The scaling exponents over both epsilon(r) and r for the condition ally averaged velocity increments delta(r)u\epsilon(r) are quantified, and the direction of their variations conforms with the refined simil arity theory. The dimensionless averaged velocity increments (delta(r) u(n)\epsilon(r))/(epsilon(r)r)(n/3) are found to depend on the local R eynolds number Re-epsilon r = epsilon(r)(1/3)r(4/3)/v in a manner cons istent with the refined similarity hypotheses. In the inertial subrang e, the probability distribution of delta(r)u/(epsilon(r)r)(1/3) is fou nd to be universal. Because the local Reynolds number of K62, R(epsilo n r) = epsilon(r)(1/3)r(4/3)/v, spans a finite range at a given scale r as compared to a single value for the local Reynolds number R(r) = e psilon(-1/3)r(4/3)/v in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence held at moderate Taylor microscale (glo bal) Reynolds number R(l)ambda. Consequently universal constants in th e second refined similarity hypothesis can be determined quite accurat ely, showing a faster-than-exponential growth of the constants with or der n. Finally, some consideration is given to the use of pseudo-dissi pation in the context of the K62 theory where it is found that the pro bability distribution of locally averaged pseudo-dissipation epsilon(r )' deviates more from a log-normal model than the full dissipation eps ilon(r). The velocity increments conditioned on epsilon(r)', do not fo llow the refined similarity hypotheses to the same degree as those con ditioned on epsilon(r).