Energy spectrum (sea)

A sea energy spectrum, S(omega), gives the distribution of wave energy across frequency, so that S(omega) d-omega is the variance contribution of wave components in the band d-omega and the area under the curve equals the sea-surface variance. The significant wave height follows as H_s = 4 times the square root of m_0, where m_0 is the zeroth spectral moment (the area), and the n-th moment m_n equals the integral of omega-to-the-n times S(omega). Standard forms include Pierson-Moskowitz for fully developed seas and JONSWAP for fetch-limited seas; a directional spectrum adds a spreading function in heading. Spectral moments feed Rayleigh-based short-term statistics for motions and loads.