NONLINEAR AND WAVE THEORY CONTRIBUTIONS OF T. BROOKE BENJAMIN (1929–1995)

Abstract

Brooke Benjamin's original theories of fluid mechanical phenomena changed our basic understanding of cavitation bubbles, surface and internal waves, gravity currents, instabilities of shear flow over flexible surfaces, and swirling flows. For some types of finite-amplitude wave phenomena, he generated integral constraints and derived new partial differential equations; by establishing their general properties he showed how they have wide application. He developed a complementary approach based on functional analysis that was quite new to fluid mechanics. He demonstrated methods for deriving, without detailed calculation, the essential features of nonlinear and indeterminate flow problems that are otherwise intractable.