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 (10)

• An optimal shell model of turbulence
• Analytic Study of Shell Models of Turbulence
• A Note on the Regularity of Inviscid Shell Model of Turbulence
• An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
• Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy
• The vanishing viscosity limit for a dyadic model
• Stochastic attractors for shell phenomenological models of turbulence
• Anomalous scaling in a shell model of helical turbulence
• Uniqueness for a Stochastic Inviscid Dyadic Model
• Energy dissipation and self-similar solutions for an unforced inviscid dyadic model