Wave Energy Flux Calculator

Wave energy flux, usually called wave power, is the rate at which a wave train carries energy across a line one metre wide perpendicular to its travel direction. It is the product of two quantities: the depth-averaged energy density E = rho g H squared / 8, which for seawater at 1025 kg/m3 sums equal parts kinetic and potential energy, and the group velocity Cg, because energy travels with the group rather than with individual crests. In deep water Cg is half the phase speed, so P = rho g squared H squared T / (64 pi), which reduces to the useful rule of thumb that power in kW/m is about 0.49 times significant wave height squared times period. A 2 m, 8 s sea delivers roughly 16 kW/m; a 4 m, 12 s Atlantic swell close to 94 kW/m. Developers classify sites by annual mean flux: below about 5 kW/m is not worth pursuing, 15 to 30 kW/m is moderate, and above 60 kW/m is excellent. Real annual means run near 70 kW/m west of Ireland and Scotland, 40 to 50 kW/m off Oregon and southern Chile, and under 10 kW/m in the Mediterranean and most of the tropics. The formula is linear theory and assumes deep water unless group velocity is corrected for depth, so nearshore values fall after bottom friction and breaking losses. A single height and period ignores the spectral spread of a real sea, where the energy period Te rather than the peak period belongs in the equation. Resource is not yield: a converter recovers only a fraction of the incident flux.

Interest in extracting power from waves is far older than the modern industry. A French patent by Pierre-Simon Girard and his son in 1799 proposed using wave motion to drive machinery, and hundreds of wave-motor patents were filed in the United States and Europe through the nineteenth century, several built along the California coast around 1900. None survived long, because the same storms that supply the energy destroy the machinery. The physical basis for calculating the resource arrived separately, through the linear wave theory of George Biddell Airy in 1841 and the recognition that energy propagates at group velocity, a concept clarified by George Gabriel Stokes and by Lord Rayleigh in the 1870s. Serious engineering assessment began after the 1973 oil crisis. Stephen Salter at the University of Edinburgh published his nodding duck converter in Nature in 1974, and the United Kingdom ran a government wave energy programme through the late 1970s and early 1980s that produced the first systematic resource maps of the northeast Atlantic. Yoshio Masuda had already commercialised oscillating water column navigation buoys in Japan from the 1960s. Long-term resource statistics became reliable once buoy networks and satellite altimetry accumulated records, and the International Electrotechnical Commission published IEC technical specifications in the 62600 series from around 2015 that standardise how wave energy resource is characterised, including the use of significant height and energy period.