Passive polymers

The feedback of polymers included in Oldroyd-B model is proportional to their concentration $n$ through the parameter $\eta \propto n$ in Eq (4.1). In the limit $\eta =0$ polymers are passively transported and stretched by Newtonian two-dimensional turbulence. The flow is driven at the largest scales and develops an enstrophy cascade towards the small scales, while the inverse energy flux is immediately halted by friction. The ensuing velocity field is therefore everywhere smooth. According to Refs.[75,52,54] the statistics of stretched polymers in random smooth flows is expected to depend critically on the value of the Weissenberg number, here defined as

$$Wi= \lambda_N \tau$$ (4.4)

where $\lambda_N$ is the maximum Lyapunov exponent of the Newtonian flow.