David J. Benney: Nonlinear Wave and Instability Processes in Fluid Flows

David J. Benney (1930-2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrodinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition.