Momentum and energy exchange across an air–water interface. Partitioning (into waves and currents) and parameterization

Abstract

Abstract Expressions have been derived to parameterize: (a) the total (time) mean wind momentum and energy fluxes across the air–sea interface, and (b) their partition into waves and a mean surface drift current, as expressed by the fractions γ M and γ E , in terms of the wave age, c p / u * , and the significant slope, § , of the wave field. Available laboratory and field observations support the parameterization predictions. The fraction of the wave-supported momentum, γ M , increases initially with the wave age (and/or the non-dimensional fetch, x ˜ ) but, as the wave field matures, it diminishes and attains rather constant small values (of about 0.05) at large wave ages (and/or x ˜ ). For a fixed wave-age (and/or x ˜ ), γ M , increases with § . The corresponding wave-supported energy fraction, γ E , shows a similar behavior for small and moderate wave ages (and/or x ˜ ), although γ E values remain greater than about 0.5 in the range 5 ⩽ c p / u * ⩽ 10 ; yet, at larger wave ages (and/or x ˜ ), although γ E values remain greater than about 0.5 in the range 5 ⩽ c p / u * ⩽ 10 ; yet, at larger wave ages (and/or x ˜ ) γ E appears to increase again, reaching values of about 0.8 when c p / u * ≈ 30 , features, all in accord with experimental observations. For waves generated locally by wind, where c p / u * is of O(1), a significant portion of the normalized total (time) mean wind-energy flux across the interface goes directly to the surface drift current, the remaining being transferred to the waves. For mature waves or waves generated in the presence of swell, where c p / u * is of O(10), this energy partition changes, the waves now supporting more energy than the surface drift current. The relative importance of the normalized wave-energy dissipation fraction, compared with the corresponding wave-energy fraction advected by the wave field and the energy fraction supported by the drift current, is also examined as the wave field develops.