MODELING NEARLY INCOMPRESSIBLE TURBULENCE WITH MINIMUM FISHER INFORMATION

The principle of minimum Fisher information (MFI) is used to work out the joint distribution function of the density and velocity in homogen eous, isotropic, stationary, nearly incompressible turbulence. We assu me that the Mach number is very low. It is shown that simple constrain ts on the minimization may be chosen to give a good fit to the pressur e distribution function found in recent direct numerical simulations a nd experiments, where the PDF is exponential for negative p and roughl y exp[-(p/p(0))(3/2)]p(-1/2) for positive p. The appropriate constrain ts in the Mm problem are on the skewness of the PDF both by itself and weighted by the internal energy density of the fluid. MFI then predic ts that in the limit of very low Mach number, the pressure and the flu id velocity u are independent of each other, as random variables; i.e. , P(p,u)-->P(p)P(u). Also, P(u) is a Gaussian. (C) 1996 American Insti tute of Physics.