Brooke Benjamin

Abstract

Abstract Brooke Benjamin was a mathematical physicist who studied electrical engineering before switching to fluid mechanics and quickly developing an international reputation for original insights and seminal work, both experimental and theoretical. He worked on many phenomena: the collapse of bubbles, flow of liquids through articulated pipes and containers with flexible boundaries, flow of thin films down inclined planes, stability of surface and internal waves and of shear flow over flexible surfaces, the behaviour of gravity currents, and Taylor–Couette and swirling flows. These early investigations included the discovery of the eponymous Benjamin–Feir theory of stability of periodic waves, Benjamin–Lighthill theory for bores, and the Benjamin–Ono equation. Since all this work involved nonlinear equations, he invariably sought and often found universal physical principles to compensate for the fact that nonlinear equations can seldom be solved explicitly. This approach naturally led him to apply abstract mathematics to physical situations, and he became interested in how topological and variational methods, and the emerging theory of nonlinear partial differential equations (PDE), could lead, without detailed calculations, to conclusions about problems that might otherwise have been impenetrable. But he never abandoned his belief in the importance of good experimental work and was a strong advocate of the need for a close alliance of classical theory with experimental studies and modern abstract methods. He was completely committed to rigorous analysis of PDEs, as exemplified by the BBM (Benjamin–Bona–Mahony) equation.