Hogner model of wave interferences for farfield ship waves in shallow water

The remarkably simple yet realistic Hogner model of farfield ship waves, previously considered to analyze the apparent wake angle associated with the highest waves that result from constructive interferences among the divergent waves created by a fast ship in deep water, is applied to the more general case of uniform finite water depth. This theory is used to illustrate notable features of ship waves in finite water depth. In particular, numerical applications to a monohull ship and catamarans illustrate two notable features of ship waves in shallow water: specifically, the apparent wake angle can be much smaller than Havelock's classical asymptote or cusp angles, and the apparent wake angle in finite water depth is nearly identical to the apparent wake angle in deep water if the water depth is greater than the ship length. Moreover, the numerical illustrations demonstrate the paramount importance of interferences among divergent waves for fast ships. Indeed, constructive interferences among the divergent waves created by a fast ship largely determine the variation of the amplitude of the waves across the ship wake, and therefore the apparent wake angle and the wave drag of the ship, a critical element of ship design. These numerical illustrations also corroborate main conclusions of an approximate analysis of wave interferences in shallow water for monohull ships and catamarans modeled as 2-point wavemakers.