An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave marker technique

Abstract

Divergent ship bow waves were simulated experimentally with a two-dimensional wavemaker that employs a flexible wave board. The wavemaker was programmed so that the wave board created a time sequence of shapes that simulated the line of intersection between one side of the hull of a slender ship model moving at constant speed and an imaginary vertical plane oriented normal to the ship model track. The time history of the water surface shape was measured with a cinematic laser-induced fluorescence technique for eight Froude numbers (FD = U/, where U is the forward speed of the equivalent three-dimensional ship model, g the acceleration of gravity and D the ship model draft). The waves produced ranged from small-amplitude non-breaking waves at the lowest Froude numbers to plunging breakers at the highest Froude numbers. These waves are strongly forced and at the higher Froude numbers begin breaking before leaving the wave board. The time histories of various geometric characteristics of the water surface shape including the hull contact line, the wave crest, the plunging jet and the splash zone, which is here defined as both the turbulent zone on the front face of the wave in the spilling breakers and the turbulent zone generated ahead of the jet impact point in the plunging breakers, were measured. The phase speed of the primary wave generated during each run ranged from 2.56Uwl (where Uwl is the maximum speed of the wave board at the undisturbed water level in the tank) at the lowest Froude number to about 1.7Uwl at the three highest Froude numbers. The maximum heights of the primary wave, the contact point on the wavemaker and the splash zone increased in a nearly linear fashion with increasing FD. In the cases with plunging jets, the jet tip trajectory was parabolic with a vertical acceleration ranging from 0.6g at FD = 1.467 to 0.8g at FD = 1.817 (the highest Froude number).

Scattering Analysis for Ship Kelvin Wakes on Two-Dimensional Linear and Nonlinear Sea Surfaces

“…Ship-wake systems mainly include Kelvin wake and turbulent wake which are two of the most important features in target identification on the oceanic background [25,26]. The turbulent wake refers to the volume scattering of foam layers, and this paper only studies Kelvin wakes of ships.…”

“…where subscript pq denotes polarization state, and (25) Due to the random features of the rough sea surface, the final bistatic NRCS and the backscattering coefficient are calculated as an average, i.e., σ 0 pq = σ 0 pq (26)…”

Composite Scattering of Ship on Sea Surface With Breaking Waves

“…Generally the breaking initiates in the form of a large plunging jet that originates as a sheet of water, climbing up the hull just aft the stern. The energy, which is supplied by the engine of the ship, is converted from the mean flow into energy in the turbulent flow in the wakes by the breakers [30].…”

Study of Electromagnetic Scattering From Ship Wakes on Pec Sea Surfaces by the Small-Slope Approximation Theory

“…Ship wakes mainly include Kelvin wake and the turbulent wake which are two of the most important characteristics in target identification on the sea surface [22,23]. The major research on ship wakes is to analyze the geometric simulation of Kelvin wakes which are the V-type wakes composed of the divergent and transverse waves when a ship is moving.…”