THE MASS TRANSPORT VELOCITY UNDER SURFACE GRAVITY WAVES

Surface gravity waves propagating on still water cause the water particles to move in elliptical orbits that are, in general, not closed – the particles move faster in the upper half of the orbit than in the lower half, generating a net Lagrangian drift, often referred to as Stokes drift, or mass transport, in the direction of wave propagation. In an open, unbounded system, this is a Lagrangian phenomenon – the fluid velocities at any fixed point are periodic, with zero mean. But if the waves are propagating in a closed system, this Lagrangian drift must be counterbalanced by a reverse flow, in the opposite direction to that of wave propagation, and this reverse flow manifests itself as an Eulerian mean velocity. Of course, since mass must be conserved in an Eulerian frame, there must also be an equivalent Eulerian mass transport in the direction of wave propagation, and this in fact occurs at the surface, above the mean water level, where the Eulerian velocity can only be positive – water particles are lifted above the mean water level as the wave crest passes, and move forward under the wave crest; the negative return velocity occurs beneath the mean water level. This mean drift velocity plays an important rôle in a number of coastal processes, in particular those involving the transport of sediments that have been stirred up by wave action. So any numerical simulation of sediment transport in the coastal zone needs to reproduce correctly the wave-induced mass transport velocity. In most practical situations, waves approaching the coast are refracted by the gradually reducing depth, so that at the shoreline the wave crests are almost parallel to the shore. If the crests are not exactly parallel to the shore then the component of the mass transport velocity parallel to the shore line will generate a longshore transport of sediment. The limiting case is therefore that in which the waves approach the coast with the crests parallel to the coast (so the wave rays are orthogonal to the coast), and this is the case most often studied in the laboratory, for obvious practical reasons. This paper describes a numerical simulation of such a configuration, using OpenFOAM, and a comparison with data from laboratory studies of the same configuration.