A vorticity-only formulation and a low-order asymptotic expansion solution near hopf bifurcation

摘要

A vorticity-only formulation is used in order to study the behaviour of the solutions of the Navier-Stokes equations for two-dimensional incompressible flows as the reynolds number is increased. This approach allows one to limit the numerical-solution domain to the vortical re- gion of the flow, thereby reducing the number of the state variables of the system. The vorticity-only formulation is obtained from a vorticity-stream function formulation by inverting the Poisson equation relating the vorithicity to the stream function and substituting the expression for the velocity in the vorticity-transport equation.