STRONG ECHO EFFECT AND NONLINEAR TRANSIENT GROWTH IN SHEAR FLOWS

The nonlinear interaction of two disturbances excited successively in a two-dimensional Couette flow is shown to lead to a transient energy growth. This phenomenon, which is called the echo effect and exists in several other physical systems, is interesting because the energy gro wth appears long after the energy associated with the original disturb ances has decayed. Here, the echo effect is studied analytically and n umerically in a situation where the nonlinear response has the same or der of magnitude as the two excitations. A system of amplitude equatio ns describing the nonlinear interactions between three sheared modes i s derived and employed to examine the physical mechanism of the echo. The qualitative validity of this system is confirmed by numerical simu lations. The influence of viscous dissipation on the echo effect is al so considered. (C) 1998 American Institute of Physics.