Accurate determination of internal kinematics from numerical wave model results

The internal kinematics for surface waves propagating over a locally constant depth are expressed as convolution integrals. Given the wave kinematics at the still water level (SWL), this provides explicit and exact potential flow expressions for the internal kinematics as convolutions in space with appropriate impulse response functions. These functions are derived in closed form and they are shown to decay exponentially. This effectively reduces the limits of the convolution integral to a horizontal distance of approximately three water depths from the water column of interest. The SWL kinematics must be provided within this region. The source of SWL kinematics may, e.g. be one of the recently developed highly accurate Boussinesq-type formulations. The method is valid for multidirectional, irregular waves of arbitrary nonlinearity at any constant water depth.