The paper studies the issue of stability of solutions to the Navier-Stokes
and damped Euler systems in periodic boxes. We show that under action of fast
oscillating-in- time external forces all two dimensional regular solutions
converge to a time periodic flow. Unexpectedly, effects of stabilization can be
also obtained for systems with stationary forces with large total momentum
(average of the velocity). Thanks to the Galilean transformation and space
boundary conditions, the stationary force changes into one with time
oscillations. In the three dimensional case we show an analogical result for
weak solutions to the Navier- Stokes equations
