Wave Interferences And Far-field Ship Waves

Ship wakes that appear to be significantly narrower than the classical 19028'Kelvin angle have long been observed for high-speed ships.The analytical and numerical studies presented here provide convincing evidence that these observations of narrow ship wakes,widely reported in the literature,correspond to the highest waves that result from constructive interferences among the divergent waves created by a ship bow and stern at high Froude numbers,for which divergent waves dominate transverse waves.Wave-interference effects on far-field ship waves are analyzed here both for deep water and for the more general,and considerably more complicated,case of shallow water?of uniform finite depth?.Moreover,both elementary analytical flow models in which a ship is modeled as a 2-point wavemaker,or?for a catamaran? as a 4-point wavemaker,and more precise numerical flow models based on distributions of sources over the ship hull surface are considered.Specifically,the 2-point wavemaker model of a monohull ship consists of a point source at the bow and a point sink at the stern,the 2-point model of a catamaran consists of a pair of point sources?or sinks? at the twin bows?or sterns? of the catamaran,and the 4-point model of a catamaran consists of two sources at the bows and two sinks at the sterns of the catamaran.These simple ship models contain important information about far-field ship wakes that cannot be found in the classical 1-point wavemaker model?which evidently cannot account for wave-interference effects? commonly used since Kelvin.Moreover,these analytical models provide basic insight and simple analytical relations from which a number of useful conclusions can be drawn.Several major conclusions,corroborated by the numerical analysis for the more precise flow model based on hull-surface distributions of sources also considered in the thesis,are now noted.The apparent wake angle associated with the highest waves that result from constructive interferences among the dominant divergent waves created?predominantly? by the bow and the stern of a ship?monohull ship or catamaran? that travels at a high Froude number in calm water can be significantly smaller than Kelvin's classical 19°28' cusp angle?for deep water? or Havelock's cusp or asymptote angles?for shallow water?.Thus,wave-interference effects provide a particularly simple explanation for the observations of narrow ship wakes?small apparent wake angles? reported in the literature.Longitudinal interferences between the divergent waves created by sources and sinks distributed over the fore and aft of a ship are dominant for common monohull ships.However,lateral interferences between the waves radiated by sources?or sinks? distributed over the port and starboard sides of a monohull ship,or over the two hulls of a catamaran with identical twin hulls,are increasingly important as the Froude number increases,and actually dominate longitudinal interferences for catamarans even at?relatively low? Froude numbers greater than about 1.Indeed,the dominance of lateral interferences for catamarans,even at relatively low Froude numbers,explains why the extremely simple model of a catamaran via two point sources at the twin bows of the catamaran?or two point sinks at the sterns? is accurate for a surprisingly broad range of Froude numbers,specifically for 1<F?V/gL^1/2 where V and L denote the speed and the length of the ship and g is the gravitational acceleration.However,a 4-point wavemaker model?two point sources at the twin bows and two point sinks at the sterns? is necessary to also account for longitudinal interferences,important for F<1.The influence of lateral interferences also explains why differences between the classical Michell and Hogner flow models are significantly smaller for a catamaran,for which lateral interferences between the twin hulls of the catamaran overwhelm lateral interferences between the port and starboard sides of the hulls,than for a monohull ship.The apparent wake angle associated with the highest divergent waves that result from constructive interferences can be approximated quite well by means of a 2-point model for a monohull ship?a source near the bow and a sink near the stern?or a 4-point model for a catamaran?a pair of sources near the bow and a pair of sinks near the stern?if the distance between the bow source and stern sink?or the pair of sources and sinks?is properly chosen.These elementary ship models show that differences between the amplitudes of the bow and stern waves have no influence on the occurrence of constructive or destructive interferences,although they affect the intensity of wave-interference effects,which are strong if the amplitudes of the bow and stern waves are commensurate or weak otherwise.The highest waves that result from wave interferences are much shorter than the waves found at the cusps or the asymptotes of the Kelvin-Havelock wake.Consequently,whereas the Havelock cusp and asymptote angles are greatly influenced by the Froude number based on the water depth,the apparent wake angle associated with the highest ship waves is only significantly affected by the water depth in very shallow water.Specifically,the highest waves that result from constructive interference effects among the waves created by a fast ship in deep water,and the related apparent wake angles,can be experimentally investigated in a towing tank for a ship model of length smaller than the depth of the tank.This conclusion is of practical interest for experimental observations of the highest waves within the Kelvin wakes of fast ships in deep water.Indeed,although observations of narrow ship wakes have been widely reported in the literature,reliable systematic experimental observations are not available.