Infinite-dimensional turbulence

Abstract

The authors have investigated infinite Reynolds number homogeneous isotropic turbulence for space dimensions d to infinity looking for possible simplifications. The calculations were done using both short-time expansions and renormalised expansions. For d to infinity non-linear interactions become confined to triads of wavevectors having one right angle. To all orders in perturbation the spectrum of the kinetic energy per mass has a finite limit provided a rescaled time tau =t/ square root d is used. It is shown that the incompressibility constraint does not drop out in infinite dimensions.