Scaling behaviour in a hyper-viscous Navier-Stokes equation with random initial conditions

Abstract

The Navier-Stokes equation describes the deterministic evolution of incompressible fluids. The effects of random homogeneous isotropic initial conditions on freely decaying solutions of this equation with a hyper-viscous force are studied. It is shown that there is an infrared stable fixed point for multimodal local initial conditions, accessible within the ϵ expansion, about d c = 4. This fixed point has the property that the viscosity and (an infinite number of) long-range random initial condition perturbations appear as relevant operators.