Wind-Generated Wave Height from Fetch
Fetch-limited significant wave height, peak period, and the wind duration required to reach it.
Example
You enter
- Wind speed (mph, at 10 m over water, duration-averaged -- not a raw anemometer reading) 40
- Fetch length (miles) 5
- Alternative fetch (miles) 10
- Alternative wind speed (mph) 60
You get
- Adjusted wind speed 24.6444
- Dimensionless fetch 129.973
- Wave height m 1.12931
- Significant wave height 3.7 ft (1.13 m)
- Peak period 3.6356
- Wind duration required 1.23188
- At the alternative fetch 5.2 ft -- 41% taller for 100% more fetch
- Alternative fetch increase (%) 41.4214
- At the alternative wind 6.1 ft -- 65% taller for 50% more wind
- Alternative wind increase (%) 64.6616
Checked against published worked examples from: US Army Corps of Engineers, Coastal Engineering Research Center.
Details, formula, and sources
ScopeThe worked 40 mph wind over 5 miles makes 3.7 ft at 3.6 s and needs 1.23 hours to build, so a squall produces far less. A hindcast, not a forecast; a measured record governs.
Formula or tableU_A = 0.71 U^1.23 (U in m/s); X = g F / U_A^2; H_mo = 0.0016 sqrt(X) U_A^2 / g; T_p = 0.2857 X^(1/3) U_A / g; duration t = 68.8 X^(2/3) U_A / g.
Source and editionThe Shore Protection Manual fetch-limited deep-water growth relations. A measured wave record where one exists, and shoaling and refraction at the site, govern.
Free accessPublished by the US Army Corps of Engineers and freely available.
What governsEstimate. AHJ and licensed professional govern.
API field nameswind_speed_mph, fetch_mi, alternative_fetch_mi, alternative_wind_speed_mph, adjusted_wind_ms, dimensionless_fetch, wave_height_m, wave_height_ft, peak_period_s, duration_required_hr, alternative_fetch_height_ft, alternative_fetch_increase_pct, alternative_wind_height_ft, alternative_wind_increase_pct
- Duration the term most often left out and frequently what governs; a squall does not build the wave its speed and fetch would suggestspec-v1836 method
- Water deep-water growth over a uniform fetch; shoaling and refraction are not modelledShore Protection Manual
- Fully developed sea growth stops at gH/U_A^2 = 0.2433 (period 8.134 U_A/g, duration 7.15e4 U_A/g), reached near a dimensionless fetch of 23,000Shore Protection Manual (1984) eq 3-42