 Closed-streamline threshold for a Gaussian disturbance in uniform flow

For total streamfunction $\Psi =-Uy+A{e}^{-(x^2+y^2)/a^2}$, the maximum opposing zonal disturbance speed is $\sqrt{2/e}|A|/a$. Below the displayed threshold the zonal velocity never changes sign and streamlines cannot close. Above it two stagnation points appear on the symmetry axis: one has definite Hessian and is a center, the other has indefinite Hessian and is a saddle. Closed contours surround the center. Equality is a degenerate onset, not a finite-area closed-cell regime.