ON NARROW V-LIKE SHIP WAKES

This paper is concerned with the generation of short gravity waves and their radiation from the outer edge of the turbulent boundary layer a nd wake of a ship. They arise primarily near the ship's stern. The wav e spectrum in the direction of wavenumber vector at an angle (90 degre es - delta) to the ship's track is: Phi(delta)(omega) = Psi(UTd/2l, U sin delta/C-g, R/UTd)1/k(0)R 2l omega(2)/g(2) Upsilon(0,pi/l;0,omega), where Psi is dimensionless and a function of three dimensionless para meters. Upsilon is the spectrum of the oscillating motion at the bound ary, U the ship speed, T-d the decay timescale of the oscillating moti on, 2l the lengthscale of the eddies, and R the distance away from the boundary along the wavenumber vector. Generally, Phi(delta), has larg e values near delta = 0 and small values at large delta; 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 distan ces 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 a lso applicable to various problems of surface wave generation by turbu lence in water.