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Motivation
Ocean currents are responsible for the transport of heat, salt, nutrients, pollution, tracers and sediments in the sea. They affect human life on earth in many ways, ranging from their impact on the global climate to their importance for the local coastal environment.
The surface currents in the ocean are mainly driven by the wind. Since the density of the air is about one thousand times less than the density of water, a momentum balance between the atmosphere and the ocean in the case of a standard wind of 10 m/s at sea level would imply an ocean current of the order 1 cm/s. However, in order to model ocean currents in a quantitative way, it is not sufficient to consider the mean horizontal shear stress from the wind on the ocean surface. This is because the action of the wind inevitably will lead to the generation of surface waves which themselves possess mean horizontal momentum, that is, the so-called Stokes drift. So, in order to obtain the total current, we must study the wave problem as well. Although it is nearly 150 years since Stokes published his theory on wave-induced drift and more than 90 years since Ekman developed his theory for stress-induced currents in the ocean, the more holistic approach of considering these phenomena as two sides of the same problem is still in its infancy. This approach will be adopted in the present project, and we will persue it by using so-called Lagrangian, or particle-following formalism, e.g. Weber and Melsom (1993a) for the coupled growing-wave/wind-drift case.
One of the most intriguing problems encountered in this area is the occurrence of wave breaking. In this situation a considerable momentum flux is lost from the waves; see for example Melville and Rapp (1985) for mechanically generated waves. In the ocean it is the presence of wind that causes wave growth, as first sucessfully explained by Miles (1957) and Phillips (1957). When the waves become sufficiently steep, they break; for an updated approach we refer to Jenkins (1994). Thus, the wave amplitude is reduced within a relatively short time interval. The continued action of the wind causes the waves to rebuild and break and so on. In a statistical sense, then, the sea may become steady, or saturated (Toba 1973, Phillips 1985). In this case there must, in an average way, be a balance between the energy input from the wind and the dissipation due to wave breaking. Recently, J. E. Weber and A.Melsom, where the latter now works at the suggested collaboration partner DNMI, have shown theoretically that the momentum transfer from the atmosphere to the upper ocean via growing/breaking waves is of the same order of magnitude as that due to the mean wind stress (Weber and Melsom 1993b) as far as the volume flux is concerned.
Papers
Jan Erik Weber: "Virtual wave stress and mean drift
in spatially damped surface waves". Submitted for publication, 2000
Background and motivation
The concept of virtual wave stress (VWS) is applied
to spatially damped, deep-water surface gravity waves. With particular
emphasis on laboratory wave tank measurements, it is pointed out that
VWS induces a mean Eulerian drift current that increases in time. This
can be important for the determination of the wave-induced drift
current, especially when the surface contains thin slicks of
contaminating material. A novel formulation is derived that relates VWS
to the lateral divergence of the mean wave momentum flux. It is
suggested that this formulation can be helpful in determining the mean
drift current in the presence of surface slicks as well as the mean
volume flux associated with deep-water waves that break in a limited
spatial region
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