On the Growth of the Spectrum of a Wind Generated Sea According to a Modified Miles-Phillips Mechanism

摘要

A linear differential equation for the change of spectral density can be expressed by d/dt S(omega; u,x,y,t) = A(omega, u(t,x,y)) + B(omega, u(t,x,y)) S(omega; u,x,y,t) where S(omega; u,x,y,t) is the spectrum, and the terms A(omega, u(t,x,y)) and B(omega, u(t,x,y)), can be considered to be due to the Phillips type of resonance and the Miles surface instability growth theory, respectively. To determine these functions, the spectra computed from wave records obtained by the British weather ships, 'Weather Reporter' and 'Weather Explorer' were used. Also, to make up for the lack of a full range of those data, results obtained in the field study of Snyder and Cox were used. The spectral growth equation was then extended by an appropriate assumption for energy dissipation. The derived spectral growth agrees with the growth of waves obtained by Sverdrup and Munk in the wave height sense, and the spectra grow in roughly the way postulated by Neumann. The results of this study show that about 30 hours are required to reach 90% of the fully developed significant wave height for a 40 knot wind measured at 19.5 m. Also about 600 nautical miles are needed for 90% full development for a 40 knot wind velocity at 19.5 m. The family of partially developed sea spectra is shown for wind velocities from 20 knots to 45 knots in 5-knot increments for both the duration limited and fetch limited conditions. (Author)