INTERACTION OP A DISTRIBUTED SURFACE VIBRATION WITH AN ADJACENT STEADY FLUID FLOW

摘要

An analysis is presented describing, in an idealized manner, the oscillatory flow field generated in viscous fluid supported by a flat plate, when the plate surface is excited into a transverse standing wave pattern by external means. The analysis proceeds to include the influence of a constant D.C. flow on the oscillatory fluid motion for the case of both standing and travelling surface waves. The ultimate aim of such studies has been to ascertain whether or not the transition of a laminar flow into turbulent flow could be delayed by active excitation of the boundary;or, whether or not such oscillation can modify the turbulent flow field should transition occur. Of particular interest are results of the analysis which explain, in principle, certain experimental results reported by Schilz and Mechel at the III Physikalisches Institut, Gottingen. A brief description of these results is included in an Appendix to the present report. Finally, an attempt is made to include the effects of the steady flow boundary layer profile on the total flow field, by a piecewise superposition of adjacent constant velocity layers of increasing magnitude as the distance from the boundary increases. This idealized model suggests qualitatively the conditions under which amplification of the boundary layer disturbances produced by the vibrating surface may occur, as they are transmitted through a steady flow boundary layer.