Effects of wave interference on farfield ship waves in shallow water

摘要

Effects of wave-interference on the far-field waves created by a ship, oflength L, that advances at constant speed V along a straight path in calmwater of uniform finite depth D are analyzed. Specifically, the apparentwake angle ψ_(max) that corresponds to the ray angles ψ = ±ψ_(max) wherethe largest waves are found is determined for a monohull ship or a catamaranat high Froude numbers F ≡ V/√gL or Fs ≡ V/√gS, where g and S denote the acceleration of gravity and the lateral separation distancebetween the two hulls of the catamaran. The monohull ship orthe catamaran are approximated as 2-point wavemakers. This simple approximationmodels the dominant waves created by the bow and the sternof a monohull ship, or by the bows (or sterns) of the twin hulls of a catamaran.The study extends the analysis previously reported for deep waterto the more general, and considerably more complicated, case of shallowwater. The analysis shows that the basic apparent wake angles ψ~x_(max) andψ~y_(max) that result from constructive longitudinal (x) interference betweenthe bow and stern waves of a monohull ship, or from constructive lateral(y) interference between the twin bow (or stern) waves of a catamaran,can differ greatly from the cusp or asymptote angles associated with theclassical far-field wave patterns of a ship in shallow water if interferenceeffects are ignored. Thus, longitudinal (x) and lateral (y) wave interferencehave very large effects on the far-field waves created by a shipin shallow water, and therefore cannot be ignored. The analysis providesbasic insight into wave-interference effects on far-field ship wavesin shallow water, and moreover yields useful practical relations.