Far-Field Features of the Kelvin Wake
DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD
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The classical Kelvin wake trailing a ship advancing at constant speed in calm water is studied. In particular, asymptotic expressions for determining the far field wake, at large distances behind the ship, are investigated numerically. This analysis indicates that the divergent waves of a surface ship generally are infinitely steep at the track of the ship, even though their amplitude vanishes there this result is theoretically possible because the wavelength of the divergent waves vanishes at the track of the ship. Inasmuch as infinitely steep water waves cannot exist in reality, the linear no surface tension analysis presented in this study suggests that no divergent waves can exist within a certain region in the vicinity of the track of the ship, and that the Kelvin wake contains three distinct regions an inner region where only transverse waves can exist an outer region where both transverse and divergent waves are present and an intermediate region at the boundary between the inner and outer regions where short steep divergent waves, as well as transverse waves, can be found. Numerical results for a simple bow form show that the inner region is quite narrow, and that the wavelength of the divergent waves at the boundary of the inner region is of the order of 1 to 20 cm, depending on the speed of the ship. These results to be consistent with the narrow V-wakes observed in some SAR images of ship wakes. The small wavelengths mentioned above indicate that the divergent waves in the vicinity of the track of the ship are likely to be significantly altered by surface tension, which must be included in a more realistic analysis.
- Fluid Mechanics