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Pierson-Moskowitz Spectrum Value

One-point PM spectrum S(ω) = α·g²/ω⁵ · exp(−β·(ω_p/ω)⁴). Used for fully-developed seas.

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Formula, assumptions, and limits

S(ω)=αg2ω5exp ⁣[β(ωpω)4]S(\omega) = \frac{\alpha g^2}{\omega^5} \exp\!\left[-\beta \left(\frac{\omega_p}{\omega}\right)^4\right]
SymbolMeaningUnit
ααPM constant 8.1e-3
ββPM shape 1.25
ωp\omega_pPeak frequency = 0.879·g/Vrad/s

Source: Pierson-Moskowitz (1964)

In short

One-point PM spectrum S(\u03c9) = \u03b1\u00b7g\u00b2/\u03c9\u2075 \u00b7 exp(\u2212\u03b2\u00b7(\u03c9_p/\u03c9)\u2074).

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