Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law
Abstract
The aim of this work is understanding the stretching mechanism of stochastic models of turbulence acting on a simple model of dilute polymers. We consider a turbulent model that is white noise in time and activates frequencies in a shell N≤ |k|≤ 2N and investigate the scaling limit as N→ ∞, under suitable intensity assumption, such that the stretching term has a finite limit covariance. The polymer density equation, initially an SPDE, converges weakly to a limit deterministic equation with a new term. Stationary solutions can be computed and show power law decay in the polymer length.
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