Waves Generated by a Moving Point-Source within a Finite-Depth Ocean

Details Waves Generated by a Moving Point-Source within a Finite-Depth Ocean Waves Generated by a Moving Point-Source within a Finite-Depth Ocean

Mar 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991em%26p...52..233l&link_type=abstract

Earth, Moon and Planets, Volume 52, Issue 3, pp.233-252

Computer Science

Scientific paper

We consider a flat ocean of finite depth h consisting of an inviscid, incompressible fluid with no surface tension. A source of constant strength moves uniformly in a horizontal direction at a constant depth. We study the wake generated by this moving disturbance. Using the Fourier transform approach, we determine the unique velocity potential for this irrotational, steady motion, subject to the bottom and free-surface boundary conditions and to its vanishing at infinity. We use an asymptotic expansion due to Poincaré to determine the elevation of the ocean surface at large distances R from the moving source along any direction displaced by a β angle from the direction of motion.
We determine analytically the number and type of waves constituting the wake; we find:
(1)
if Σh > 1 (Σ = g/u 0 2, u 0 being the constant velocity), the semi-aperture β* of the wake is always larger than the Kelvin value (~19‡) but can never reach 90‡; for 0 < β < π/4 the wake consists of a transverse and a diverging wave, but for β ⩾ π/4 we get two transverse waves;
(2)
for Σh ⩽ 1, we get β* = π/2 - θ0 where cos2 θ0 = Σh ⩽ 1; thus, β* = π/2 only when Σh = 1; for 0 < β < π/4 we get only one diverging wave, but this will transition to a transverse wave for β ⩾ π/4;
(3)
within the wake region, the elevation of the wave is of the R -1/2 order.

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