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We study the asymptotic behavior and the asymptotic stability of thetwo-dimensional Euler equations and of the two-dimensional linearized Eulerequations close to parallel flows. We focus on spectrally stable jet profiles$U(y)$ with stationary streamlines $y_{0}$ such that $U'(y_{0})=0$, a case thathas not been studied previously. We describe a new dynamical phenomenon: thedepletion of the vorticity at the stationary streamlines. An unexpectedconsequence, is that the velocity decays for large times with power laws,similarly to what happens in the case of the Orr mechanism for base flowswithout stationary streamlines. The asymptotic behaviors of velocity and theasymptotic profiles of vorticity are theoretically predicted and compared withdirect numerical simulations. We argue on the asymptotic stability of theseflow velocities even in the absence of any dissipative mechanisms.

Large time behavior and asymptotic stability of the two-dimensional Euler and linearized Euler equations