Surface films and wind wave growth

Abstract

The generation and growth of surface water waves by the wind and including modified boundary conditions appropriate for the presence of surfactants at the surface are reconsidered using linear instability theory to describe the process. The new features of our work are the inclusion of both surfactants and a wind drift layer. We allow a coupled mean flow in both the air and water; the depth‐dependent mean flow is considered to be wind‐induced. The complex wave frequencies are determined numerically. Uncontrolled numerical errors associated with a direct numerical solution of the Orr‐Sommerfeld equation for the coupled mean flow are avoided by solving an associated equation obtained by a Riccati transformation of the original equation, allowing a straightforward and efficient determination of the eigenvalues of the linear stability problem. A different aspect of our analysis is the change of surface boundary conditions due to contamination of the surface, notably, the change of tangential stress at the surface due to surface tension gradients induced by the film (known as the Marangoni effect). Comparisons are made with previous work on both film‐free and contaminated surfaces. The dominant effect of introducing film boundary conditions is a large change in the wave number of the most unstable wave with an attendant reduction in the growth rate. Implications for wind wave growth on the ocean are discussed.

Polarimetric Analysis of Backscatter From the Deepwater Horizon Oil Spill Using L-Band Synthetic Aperture Radar

“…A rigorous theoretical analysis of wind wave growth in the presence of a surface film is given by [39]. Further consideration of ( 5) and ( 6) sheds light on the general damping mechanism.…”

An experimental study of surfactant effects on spilling breakers

“…Field and laboratory experiments (Cox & Munk 1954;Lombardini et al 1989;Barger et al 1970;Hühnerfuss et al 1983;Ermakov et al 1986;Tang & Wu 1992;Bock et al 1999;Uz et al 2002;Mitsuyasu & Honda 1984) have shown that surfactants reduce the high-frequency part of the windwave spectrum. The effects of the film elasticity and surface viscosity on wind-wave growth and damping rates were studied numerically by Creamer & Wright (1992), who showed that the damping rate is substantially increased by the film elasticity and that the effect of the surface viscosity is more pronounced at larger wavenumbers when the surface elasticity is small. Lucassen (1981) demonstrated that the surfacedilational modulus has a considerable effect on the damping of short gravity waves and gravity capillary waves.…”

Studies of the Deepwater Horizon Oil Spill With the UAVSAR Radar

“…The change in surface tension can also affect the longer wavelength components of the ocean wave spectrum through gradients in the surface tension (Marangoni effect) and indirectly through nonlinear wave-wave interactions that shift energy between different wavenumber components of the spectrum [Alpers and Hühnerfuss, 1988;Gade et al, 1998aGade et al, , 1998b. A rigorous theoretical analysis of wind wave growth in the presence of a surface film is given by Creamer and Wright [1992].…”