Drift of an Inextensible Sheet Caused by Surface Waves

Abstract

Inextensible films are often used to simulate surface-active material as commonly found at sea. It is important to understand the mechanism behind wave-induced transport of surfactants with regard to e.g. oil spills in coastal areas. In this paper we compare theory, based on a Lagrangian description of motion, with observations of the wave-induced drift of thin inextensible plastic sheets in a controlled laboratory experiment. It is found that the analytical solution is able to reproduce the observed drift. In a laboratory situation with continuously generated, spatially damped waves, the drift velocity increases in time. Hence earlier theoretical treatments in which a steady state is assumed predict too low values of the drift velocity. The need for data on the time development of the drift is pointed out.

Evolution of ocean slicks under a rising wind

“…A final consideration is the role slick width may play in modifying the slick contrast. For example, very wide slicks may have a diminished wave spectrum [ Wu , 1983; Christensen and Weber , 2005] or lower surface wind stress [e.g., Wei and Wu , 1992], so that these effects could potentially increase the value of β * and hence T′. Run 4 was ideal for investigating this question because several long, well‐defined slick bands lay beneath the flight track.…”

“…In the case of a slick, the surface drift can be enhanced over that in the ambient through elastic damping of surface waves by the slick. Momentum lost from these damped waves is regained as a mean Eulerian current, which then advects the slick downwind at a speed faster than the ambient surface [e.g., Wu , 1983] The effect becomes significant only when a slick is sufficiently wide in the along‐wind direction [ Christensen and Weber , 2005]. So, similar to the oil spill, an enhanced drift can give rise to a leading‐edge appearance of a slick band while interaction with Langmuir circulation can create a feathered trailing edge.…”

Do we observe Gerstner waves in wave tank experiments?

“…(37) as a function the dimensionless Stokes surface drift u S0 /ε 2 C. The wavelength is 1.56 m, and the surface is covered by an inextensible film. The data (circles, diamonds, and squares) are from [5], and the black lines are computations of the surface drift for spatially damped Stokes waves [10]. true, since we here have shown that the effect of viscosity modifies the Gerstner wave in such a way that it induces a forward motion at the surface, while conserving total (zero) mean momentum.…”

“…The black lines are computations from [10] for spatially damped Stokes waves in the presence of an inextensible film. The various curves depict the solution after 5, 10, and 50 s, respectively.…”

“…Then it enforces a noslip condition on the horizontal part of the orbital wave motion. This generates a strong vorticity in the viscous surface-boundary layer, and leads to the development of a mean drift velocity that moves the film [8][9][10].…”