Wind–wave stabilization by a foam layer between the atmosphere and the ocean

Abstract

The study is motivated by recent findings of the decrease in the momentum transfer from strong winds to sea. The Kelvin-Helmholtz instability (KHI) of a three-fluid system of air, foam and water is examined within the range of intermediately short surface waves. The foam layer thickness necessary for effective separation of the atmosphere and the ocean is estimated. Due to high density contrasts in the three-fluid system, even a relatively thin foam layer between the atmosphere and the ocean can provide a significant stabilization of the water surface by the wavelength shift of the instability towards smaller scales. It is conjectured that such stabilization qualitatively explains the observed reduction of roughness and drag.

An asymptotic model for the Kelvin–Helmholtz and Miles mechanisms of water wave generation by wind

“…Such an expansion is a direct result of the assumptions expressed in estimations (14), that both the wave number as well as the wind velocity are of zeroth leading order in ǫ. However, as the wave lengths and the wind velocity increase, the asymptotic expansion (25) loses its validity.…”

“…To further develop the asymptotic solution in the region of nonuniformity, it is recalled that the classical KH mode (vortex sheet instability) has the following orders in terms of the characteristic length L g ( e.g. [14]):…”

“…Finally note that the assumption (14) for the asymptotic orders of the values correspond to the outer solution in terms of the method of matched asymptotic expansions [20], while within the region of nonuniformity (26) or (27) of the corresponding outer asymptotic solution (Miles' mode) the inner solution should be constructed.…”

Generation of intermediately long sea waves by weakly sheared winds

“…In Ref. 5, the system has been modelled by a three-fluid system of the foam layer sandwiched between the atmosphere and the ocean, by distributing the foam spots homogeneously over the ocean surface. In the present study, the problem is reduced to modeling of the wind waves over the foam-free portion of the ocean surface, under the effect of the logwind profile averaged over alternating foamfree and foam-covered portions of the ocean surface.…”

“…Different physically significant characteristics of the logarithmic wind may be expressed to one another for any fixed value of 10 U . For instance, the drag coefficient From the first of relations (5) follows that if one of the values a L / 10 L and d C has a maximum, another one should reach its maximum at the same value of 10 U . Since Charnock' coefficient is equal, up to a constant factor, to dimensionless roughness, it may be obtained by comparison of the generalized Charnock' formula 4 with Eq.…”