↑ The energy flux is P = 1 16 ρ g H m 0 2 c g , {\displaystyle P={\tfrac {1}{16}}\rho gH_{m0}^{2}c_{g},} with c g {\displaystyle c_{g}} the group velocity, see Herbich, John B. (2000). Handbook of coastal engineering. McGraw-Hill Professional. A.117, Eq. (12). ISBN978-0-07-134402-9. The group velocity is c g = g 4 π T {\displaystyle c_{g}={\tfrac {g}{4\pi }}T} , see the collapsed table "Properties of gravity waves on the surface of deep water, shallow water and at intermediate depth, according to linear wave theory"in the section"Wave energy and wave energy flux" below.
↑ Here, the factor for random waves is 1⁄16, as opposed to 1⁄8 for periodic waves – as explained hereafter. For a small-amplitude sinusoidal wave η = a cos 2 π ( x λ − t T ) {\displaystyle \scriptstyle \eta =a\,\cos \,2\pi \left({\frac {x}{\lambda }}-{\frac {t}{T}}\right)} with wave amplitude a , {\displaystyle \scriptstyle a,\,} the wave energy density per unit horizontal area is E = 1 2 ρ g a 2 , {\displaystyle \scriptstyle E={\frac {1}{2}}\rho ga^{2},} or E = 1 8 ρ g H 2 {\displaystyle \scriptstyle E={\frac {1}{8}}\rho gH^{2}} using the wave height H = 2 a {\displaystyle \scriptstyle H\,=\,2\,a\,} for sinusoidal waves. In terms of the variance of the surface elevation m 0 = σ η 2 = ( η − η ¯ ) 2 ¯ = 1 2 a 2 , {\displaystyle \scriptstyle m_{0}=\sigma _{\eta }^{2}={\overline {(\eta -{\bar {\eta }})^{2}}}={\frac {1}{2}}a^{2},} the energy density is E = ρ g m 0 {\displaystyle \scriptstyle E=\rho gm_{0}\,} . Turning to random waves, the last formulation of the wave energy equation in terms of m 0 {\displaystyle \scriptstyle m_{0}\,} is also valid (Holthuijsen, 2007, p. 40), due to Parseval's theorem. Further, the significant wave height is defined as H m 0 = 4 m 0 {\displaystyle \scriptstyle H_{m0}=4{\sqrt {m_{0}}}} , leading to the factor 1⁄16 in the wave energy density per unit horizontal area.
↑ Để xác định vận tốc nhóm, tần số góc ω được xem là một hàm của số sóng k, hoặc tương tự, chu kỳ T là một hàm của bước sóng λ.
