Statistical treatment of scalar transfer in isotropic turbulence

It has recently been known that local high-gradient regions of an advected scalar, such as temperature or mass contaminant, in a turbulent state of fluid form thin sheets, randomly oriented and moving around with turbulent motion. Here is presented a joint multifractal model for velocity and scalar dissipations in isotropic turbulence which can predict the statistical distributions of the worms, vorticity-concentrated regions, as well as the above-described scalar-gradient sheets. This model allows us to derive turbulent diffusion coefficient in isotropic turbulence scaled by Reynolds number and Prandtl number, which predominates far over molecular diffusion coefficient.