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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
12 articles.
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