The evolution of a finite-amplitude localized disturbance in an irrotational unbounded plane stagnation flow

Abstract

The evolution of a finite-amplitude three-dimensional localized disturbance, having an initial dipole Gaussian vorticity distribution, embedded in an external unbounded irrotational plane stagnation flow (U = (Ay,Ax,0)) is investigated. Using the fluid impulse integral as a characteristic of such a disturbance, the viscous vorticity equation is integrated analytically. Accordingly, the fluid impulse associated with such disturbances decays and grows exponentially along the principal axes x=y and x=-y, respectively. Numerical simulations, carried out for both linear and nonlinear disturbances at a Reynolds number of 40, confirm the above predictions. The simulations have also been compared wi..