Sub-exponential mixing of generalized cellular flows with bounded palenstrophy

Abstract

We study the mixing properties of a passive scalar advected by an incompressible flow. We consider a class of cellular flows (more general than the class in [Crippa-Schulze M$ ^3 $AS 2017]) and show that, under the constraint that the palenstrophy is bounded uniformly in time, the mixing scale of the passive scalar cannot decay exponentially.

Keywords

• mixing
• continuity equation
• flow of a vector field
• fluid dynamics
• palenstrophy