On non-causal impulse response functions related to propagating water waves

Abstract

Particular attention is drawn to the non-causality of two impulse response functions, one of which relates the excitation force on an immersed body to the incident wave elevation at the body's reference position, while the other relates the incident wave elevations at two different positions along the line of wave propagation. An explanation is proposed for the non-causality of the impulse response functions, in spite of the fact wave propagation is a causal process. An indication is given of how far ‘upstream’ the incident wave elevation should be measured in order to be able to know, with reasonable accuracy, the current heave excitation force on a floating truncated cylinder with vertical axis, given current and past wave-elevation measurements. This provides a method for wave prediction, which is required for optimum control of the oscillation of the immersed body.