Surface-wave generation by gusty wind

Abstract

Nikolayeva & Tsimring's (1986) collisionless Boltzmann model for surface-wave generation by a slowly fluctuating wind U(z, t) is transformed to an equivalent steady flow in which the wind speed in the reference frame of the wave (of speed c) is given by V(z)=〈(U−c)⁻²〉 ^−1/2, where 〈 〉 signifies a Gaussian average. This leads to a Sturm–Liouville equation for the Gaussian-averaged, complex amplitude of the wave-induced pressure. The wind-to-wave energy transfer for a logarithmic wind profile with the mean friction velocity κŪ₁ (κ=Kármán's constant), the standard deviation δŪ₁, and the roughness length z₀=ΩŪ²₁/g is determined as a function of the parameters δ and Ω (Charnock's constant) through numerical integration of a Riccati equation (derived from the Sturm–Liouville equation). The energy transfer exceeds that predicted by the quasi-laminar model (Miles 1957; Conte & Miles 1959) by as much as 20–30% for δ≈1 and c (wave speed)[lsim ]6Ū₁ but is decreased for c[gsim ]8Ū₁ and may be negative for sufficiently large c/Ū₁. These predictions contrast with the order-of-magnitude increase predicted by Nikolayeva & Tsimring.