Energy spectrum distribution of ocean wave has many discontinuous part or absorption zone. Every component, as it seems like an impulse or line spectrum of light, originates from different wave source, where it may have completely continuous distribution, but in the course of propagation its wide range contracts to narrow band. This process can be verified by Drs. Sverdrup & Munk's theory of ocean wave, namely by integration [numerical formula] The probability of existency of wave steepness P(β) must by proportional to I/[(dβ)/(dt)], so that distribution of unit spectrum E^*(β) is E(β)×P(β), where E(β) is wave energy at β and β varies from zero to infinity, which can be obtained by wave steepness curve. The ratio of wave height from cumulative energy to usually observed value or calculated from wave steepness curve is 0.953, which shows that both are almost equal to each other. These components arrive successively with suitable time intervals, so whole spectral distribution coincides approximately with that derived from wave steepness curve, which is certain envelope of indcpendent data of prominent waves at different sea surface. This fact has applied intuitiously by Dr. Neumann. The roughness factor "n", where n=2 means Dr. Longuet-Higgins's modern irregular seas and n=∞ corresponds to classical regular swells, can be estimated from next intrinsic equation: [numerical formula], or [numerical formula] where the left hand of above equation is the ratio of the prevailing wave height to total mean value and the right hand is average maximum or partial mean value. This relation leads approximately n=e^β. There can exist many roughness, and if we choose the steepness curve βδ=const. this is special case when roughness is uuiform everywhere in and outer region of storm. From the above-mentioned point of view, steepness curve must be drawn β^2δ=const, above I.4, where wave energy reaches a peak and where apart two curves of Drs. Sverdrup & Munk and Dr. Neumann. The irregularity of seas is usually larger than that of swells, so that irregularity of pitching amplitude is also larger than that of rolling. Generally speaking, irregularity of oscillations of ships are not equal even if they were on the same sea surface. However, at the present macroscopic stage, the theory of Drs. St. Denis & Pierson is still valid in rough sea surface.
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