On Nonlinear Flow with Multiple Obstructions

Abstract

Whereas long-wave theories have proved successful in describing, the nonlinear effects of single obstructions on narrow flows, the theories can fail when several obstructions are present. This failure is demonstrated using a simple laboratory flow which is predicted by long-wave theory to be unstable, but which is stability in practice by short-wave effects. A nonlinear dispersive theory leads to an interpretation of the short waves as a combination of cnoidal and solitary waves, and upstream control is found for the second (downstream) obstacle only.