Evolution of global enstrophy in cylinder wake controlled by Lorentz force

The Okubo-Weiss function is correlated with the fluid particle compression,deformation and vorticity,which provides a simple way to characterize different regions of a flow-field.In the present paper,it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries.To validate the conclusion,a flow passing a circular cylinder controlled by the electromagnetic force is calculated numerically as an example.Distributions of global enstrophy,total squared strain and Okubo-Weiss function in the controlled flow field are discussed.The influence of Lorentz force on the distribution is analyzed.