On Stochastic Shell Models of Turbulence

Abstract

We prove existence of weak and strong solutions and uniqueness for a viscous dyadic model driven by additive white noise in time using a path-wise approach. Existence of invariant measures also established and a simple balance relation among the mean rates of energy injection, dissipation and flux is derived and we investigate the asymptotic exponents ${\zeta }_p$ of the $p$-order structure functions.

References in corpus (4)

• An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
• The vanishing viscosity limit for a dyadic model
• Uniqueness for a Stochastic Inviscid Dyadic Model
• Energy dissipation and self-similar solutions for an unforced inviscid dyadic model