Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T22:09:40.475Z Has data issue: false hasContentIssue false
  • English
  • Français

On narrow V-like ship wakes

Published online by Cambridge University Press:  26 April 2006

Daifang Gu  and
O. M. Phillips
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
Get access Rights & Permissions [Opens in a new window]

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
Information
Journal of Fluid Mechanics , Volume 275 , 25 September 1994 , pp. 301 - 321
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Gu, D. 1989 On surface wave generation by boundary disturbances. PhD dissertation. The Johns Hopkins University.
Lyden, J. D., Hammond, R. R., Lyzenga, D. R. & Shuchman, R. 1988 Synthetic aperture radar imaging of surface ship wakes. J. Geophys. Res. 93, C10, 12293–12303.Google Scholar
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. John Wiley.
Michell, J. H. 1898 The wave resistance of a ship. Phil. Mag. [5] 45, 106–133.Google Scholar
Munk, W. H., Scully-Power, P. & Zachariasen, F. 1987 Ships from Space. Proc. R. Soc. Lond. A 412, 231–254.Google Scholar
Phillips, O. M. 1955 The irrotational motion outside a free turbulent boundary. Proc. Camb. Phil. Soc. 51, 220–229.Google Scholar
Shemdin, O. H. 1987 SAR imaging of ship wakes in the Gulf of Alaska. Final Rep. N00014-84-WRM-2212, Office of Naval Research, Arlinton, VA.
Shemdin, O. H. 1990 Synthetic aperture radar imaging of ship wakes in the Gulf of Alaska. J. Geophys. Res. 95, c9, 16319–16338.Google Scholar
Ursell, F. 1966 On the rigorous foundation of short-wave asymptotics. Proc. Camb. Phil. Soc. 62, 227–244.Google Scholar