Coefficient of horizontal eddy diffusion of a tracer on the water surface as a function of the wave age

A relationship between the statistical parameters of horizontal diffusion and the parameters of the energy-containing part of the frequency spectrum of sea-surface elevations is found depending on the wave age Ω and the ratio between the wind speed at 10 m and the phase velocity of the peak of a wave. It has been observed in 1–7] that the diffusion coefficient K(r) of a patch of size r increases as r ^β, where 1.15 < β < 4/3, and the patch area S(t) increases with time as t ^γ, where 2 < γ < 3. As was calculated in 15], in the energy-containing part of the elevation frequency spectrum, S(ω) ～ ω^?n , where n = 13/3 for young waves with Ω > 2, n = 4 for waves with 1.2 < ψ < 2, and n = 11/3 for developed waves with 0.83 < Ω < 1.2. It is found that β = (n + 1)/4 and γ = 8/(7 ? n). These relations explain the entire set of observed exponents: β = 4/3 and γ = 3 for young waves and β = 1.15 and γ = 2.34 for large sizes (up to 1000 km) and times (up to a month) when it is found here that β = 7/6 and γ = 2.4.