Nonlinear standing water waves generated in a closed numerical flume

Abstract

A theoretical description of fluid motion under mechanically generated nonlinear standing waves in the vicinity of a rigid vertical wall is presented. A standing wave system is formed through the interaction of mechanically driven progressive waves and waves reflected at a vertical wall, which is located at the far end of the numerical flume. An original approach is applied to provide complete information on standing wave field with respect to instantaneous velocities, particle paths and pressure. The numerical kinematics of standing waves are compared with corresponding linear, weakly-nonlinear and higher-order periodic predictions derived within the framework of the perturbation theory. An excellent agreement between the numerical and the fifth-order analytical solution results is achieved. The magnitude of dynamic pressure exerted on a vertical rigid wall is also confronted with the corresponding values acquired from simplified engineering formulas, which are used as widely accepted standards for the evaluation of hydrodynamic loads on coastal and offshore structures. An engineering diagram based on the fifth-order analytical solution constitutes a practical outcome of the study, and it allows hydrodynamic loads exerted on a vertical wall to be more accurately quantified for a wide spectrum of non-breaking wave conditions.