When the sea surface is completely smooth and there is no wave, the vertical distribution of wind velocity must be uniform, and boundary layer does not appear. However, if velocity gradient is generated, its loss of energy should contribute to the formation of wave. Applying the same idea of stationary phase to the condition of equilibrium between wave energy and energy loss of wind, following condition of sharp and steady train of wave might be reasonable, namely [numerical formula] where, H is wave height and L is wave length; ρ and ρ' are density of water and air respectively; U is uniform wind velocity outside the boundary layer thickness y=h, u(y) is velocity inside the layer. Above equation for the ratio of kinetic energy can be transformed in the form as: d^2δ/dβ^2+1/βdδ/dβ-δ/β^2=0 where δ=H/L is wave steepness, β=C/U is wave age in which C is wave velocity. From this solution, we find the fact that wave steepness is composed by two system, namely one groupe of δ∝β and the other δ∝β^<-1>. The former expressed small wind wave generated in the center of storm and is growing up by absorption of energy loss of wind. The latter corresponds to the sea state of outside the storm area; swell is propagated by the shiffing action of wind pressure. Both system crosses together at the vicinity of β=0.4 and δ=0.1, which is the maximum steepness introduced by Sverdrup and Munk, so that around the center of storm energy spectrum of wave is to be of sharply narrow banded like that of Darbyshire type, or in other words, prevailling wave motion seems to be moderately sinusoidal. Accordingly, the most severe oscillation of a ship becomes resonant state tuning into this prevailling wave. From the relation of δ∝β^<-1>, we easily derive H/H_m=U/U_m, with the aid of observed result of T=T_m, where T is wave period and suffix m denotes the value in the center of storm, we can estimate H_m and U_m in the center, which ships could not approach, from the frequency distribution or hystogram of T and H.
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