Wave-Interference Effects on Far-Field Ship Waves in the Presence of a Shear Current

Abstract

Wave-interference effects, in the presence of a shear current of uniform vorticity, are analyzed for the first time. An interesting similarity is found between the analysis of wave interferences when a linear shear current is present and that in finite depth water. In particular, wave-interference regimes exist in both analyses. The consideration of wave interferences in the presence of a shear current, for a 2-point wavemaker model of monohull ships, is shown to have interesting and nontrivial effects on ship waves, as also found in the analysis of wave interferences in finite water depth. The effect of shear on the far-field waves created by a 2-point wavemaker model of a monohull ship greatly depends on the shear Froude number Frs = VS/g, where V is the speed of the ship, S is the uniform vorticity of the shear, and g is the gravitational acceleration, as well as the angle between the shear current and the direction of motion of the ship. The Kelvin shear Froude numbers FrsK for which the ray angles of the highest waves are equal to the Kelvin angles are determined. The ray angles of the highest waves are considerably smaller than the Kelvin angles for Frs > FrsK. The presence of a shear current has significant effects on the wave interferences for the Froude number (Equation) (where L is the ship length). Conclusions drawn from the geometrical analysis in specific cases are confirmed by ship wakes obtained from the superposition of waves generated by the ship bow and stern modeled as a 2-point wavemaker. 1. Introduction Waves and currents widely coexist in coastal and offshore environments, notably in the regions of tidal, ocean, fjord, and discharge currents. Significant effects of currents on water waves have been understood for a long period, including, for instance, the effects on wave steepness and dispersive properties (Peregrine 1976; Lamb 1993). In particular, the presence of a current may cause a significant difference of drag force acting on an underdesign offshore structure (Dalrymple 1973). Furthermore, wave resistance experienced by moving ships may also be noticeably affected because of a subsurface shear current (Li & Ellingsen 2016c; Li et al. 2017). Especially, an additional lateral radiation force toward the starboard of a ship—that can amount to as much as 20% of the stern-wise wave resistance—is first introduced because of the asymmetric ship wakes (Li & Ellingsen 2016c; Li et al. 2017) resulting from a shear current. It is thereby understood that studies regarding the interplays of currents and waves are of practical significance, which are, however, scarce so far.