Analytical Approximation for Steady Ship Waves at Low Froude Numbers.
DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD
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A simple analytical relationship between a ship hull form and its steady far field Kelvin wake is obtained by considering the low Froude number limit of the Neumann Kelvin theory. In particular, this relationship predicts the occurrence of a sharp peak in the amplitude of the waves in the far-field Kelvin wake at an angle, A, from the ship track that is smaller than the Kelvin cusp angle of 1912 deg for a hull form which has a small region of flare and is wall sided elsewhere if the Froude number is sufficiently small. An explicit relationship between the angle, P, between the ship track and the tangent to the ship mean waterline in the region of flare and corresponding wave-peak angle alpha in the Kelvin is obtained. For instance, this relationship predicts the occurrence of a sharp peak in wave amplitude at an angle alpha in the Kelvin wake equal to 14 deg for a hull having a small region of flare within which the waterline-tangent angle p is approximately equal to either 30 or 74 deg. This theoretical result may explain the bright returns that have sometimes been observed in Synthetic Aperture Radar images of ship wakes at angles smaller than the Kelvin-cusp angle. The low Froude number asymptotic analysis of the Neumann Kelvin theory presented in this study also predicts that the wave resistance coefficient is order F-squared, where F is the Froude number, for a ship form with a region of flare, Order F to the 4th power for a ship form that is wall sided everywhere and has either a bow or a stern or both that is neither cusped nor round, and Order F to the 6th power for a wall-sided ship form with both bow and stern that are either cusped or round.
- Marine Engineering
- Active and Passive Radar Detection and Equipment
- Fluid Mechanics