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On narrow V-like ship wakes

Published online by Cambridge University Press:  26 April 2006

Daifang Gu
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA Present address: Program in Atmospheric and Oceanic Sciences, PO Box CN710, Sayre Hall, Princeton University, Princeton, NJ 08544–0710, USA.
O. M. Phillips
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA

Abstract

This paper is concerned with the generation of short gravity waves and their radiation from the outer edge of the turbulent boundary layer and wake of a ship. They arise primarily near the ship's stern. The wave spectrum in the direction of wavenumber vector at an angle (90° – δ) to the ship's track is: \[\Phi_{\delta}(\omega) = \Psi\left(\frac{UT_d}{2l},\frac{U\sin\delta}{c_g},\frac{R}{UT_d}\right)\frac{1}{k_0R}\frac{2l\omega^2}{g^2}\gamma\left(0,\frac{\pi}{l};0,\omega \right),\] where Ψ is dimensionless and a function of three dimensionless parameters. γ is the spectrum of the oscillating motion at the boundary, U the ship speed, Td the decay timescale of the oscillating motion, 2l the lengthscale of the eddies, and R the distance away from the boundary along the wavenumber vector. Generally, Φδ has large values near δ = 0 and small values at large δ; it behaves as 1/R at distances not far from the ship, then may vary slower than 1/R at intermediate distances, and finally behaves as 1/R again at distances far from the ship. These are consistent with the pattern found in SAR images of narrow V-like ship wakes. The method developed here is also applicable to various problems of surface wave generation by turbulence in water.

Type
Research Article
Copyright
© 1994 Cambridge University Press

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