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sci.ocean-wave-dispersion-relation Calculator
Calculates ocean wave phase speed c = √(g/k × tanh(kh)) and group velocity from water depth h and wave number k. In deep water (kh > π): c = √(g/k) — waves slow as they enter shallow water (kh < π/10) where c ≈ √(gh), causing refraction and shoaling amplification toward the coast.
Inputs
T S
Time for one complete cycle (s). Period = 1 / frequency. A 50 Hz signal has a 20 ms period.
H M
Vertical extent downward, or thickness of a layer. For tanks: affects pressure at the base (P = ρgh).
Results
deep water wavelength L₀ (m)
The computed linear length.
wavelength at depth h (m)
The computed linear length.
phase velocity c (m/s)
The current phase of the cycle or process.
group velocity Cg (m/s)
Reference formula or conversion factor shown for context.
Airy wave: ω² = gk·tanh(kh)
Sample size or count used in the calculation.
depth classification
Category assigned based on where the computed value falls on a defined scale. Check which standard or guideline defines these boundaries.