Professor Malkus will conduct experimental and theoretical studies of bounded elliptical flow in order to isolate principal mechanisms in the broad-band secondary instabilities of shearing flow. Earlier results establish that the instability is a parametric sub-harmonic resonance, whose exponential growth is limited by the transfer of angular momentum from the basic flow. It is observed that a three percent ellipticity imposed upon a ten centimeter diameter fluid-filled cylinder can catalyze a thirty percent reduction in the fluid rotation rate. This swift inertial deceleration is countered by a slow viscous spin-up, resulting in intermittent behavior in the just post-critical regime. Theoretical study will be directed towards a deductive understanding of the mechanism responsible for this highly efficient withdrawal of energy from the vortex flow. Tidal forces also cause elliptical flow. An additional aspect of this study will be the exploration of three-dimensional instabilities in stratified atmospheric, oceanic, and earth-core tidal processes. Professor Malkus will also continue the theoretical search for the deductive foundation of observed statistical stability. The success of the efficiency function as a measure of statistical stability in the channel flow offers hope for the discovery of a more general integral form. //
