Definitions of celerity for investigating surf-riding in an irregular seaway

Abstract

As is well-known, if the speed of a ship operating in high, fairly regular, following waves exceeds wave celerity, then surf-riding is realized. This motivates one to approach the calculation of the probability of surf-riding in irregular seas as a threshold exceedance problem. However, it is unknown whether such a simple phenomenological rule, using the celerity as threshold, could also be applicable for the ship dynamics associated with a stochastic wave environment. To clarify this, a suitable definition of wave celerity for an irregular seaway needs first to become available. In this chapter, we define celerity as the velocity of propagation of a fixed slope value of the wave profile. This leads to the concept of instantaneous celerity, opening up a window to the literature of instantaneous frequency in signal processing. As it turns out, instantaneous celerity is not always a consistently smooth and bounded curve. Other definitions of local celerity are also conceivable. We tested a few different selections, obtaining time-dependent celerity curves for various types of waves. Relaxing the requirement for a narrow-band spectrum, we offer some clues about the effect of spectrum’s bandwidth on celerity. In a further step, simultaneous treatment of the “wave” and “ship” processes is implemented, in order to investigate the potential of applying a local celerity condition for surf-riding’s prediction. Various patterns of ship motion, before and into surf-riding, are observed.