An examination of Kolmogorov's refined similarity hypotheses for active scalar in compressible turbulence

etc15 Tracking Number 36

Using direct numerical simulations of isotropic compressible turbulence driven by large-scale solenoidal force, we examine the Kolmogorov's refined similarity hypotheses (RSH) as applied to active scalar, i.e. temperature, with Prandtl number of order one. The three-dimensional compressible Navier-Stokes equations are solved by adopting a hybrid method for space and a second-order Runge-Kutta technique for time. The stationary turbulent Mach number, Mt, and Taylor microscale Reynolds number, Reλ, vary from 0.3 to 1.0 and 123 to 255, respectively. The two-dimensional contours of temperature dissipation field show that at low Mt the field is dominated by vortices structures while at high Mt it is full of small-scale shocklets structures. When Reλ increases, the random distribution of shocklets is reinforced, and thus, the field tends to local isotropy at small scales. According to the scaling exponents obtained in our simulations, the probability distribution of the normalized temperature increment is basically the same for the temperature fields, however, they are not close to Gaussian. Furthermore, the usage of the scaling exponents from standard RSH theory [1,2] shows that the new probability distribution behaves rather different, suggesting the failure of RSH for temperature.