A theoretical model for Langmuir circulations

Moen, Jon (1978) A theoretical model for Langmuir circulations. University of Southampton, Doctoral Thesis.

Abstract

Two recent Langmuir circulation theories (Garrett., 1976; Craik & Leibovich, 1976) are reviewed and criticised. The horizontal momentum balance for the near-surface, 'wave activity' layer is examined and a two layer model, similar to that of Hasselmann (1971), but differing in choice of separating boundary, is developed. Three predictions emerge from the analysis; firstly, a span wise periodic stationary wave of wave length equal to the windrow spacing and amplitude amounting to several centimetres is required to counterbalance horizontal gradients in the wave potential energy density, secondly, and consequently, a standing wave of wave length twice the windrow spacing is required to satisfy the horizontal momentum balance at depths below the 'wave activity' layer and, thirdly, the remaining wave stresses, consisting mostly of Hasselmann's TaIst , exert a force on the mean flow and constitute the principal driving mechanism fur Langmuir circulations. The new mechanism is developed as a wave vorticity model, whereby surface waves, initially irrotational, acquire vorticity from the mean flow vertical vorticity component and relinquish it to enhance the horizontal, Langmuir circulation component. The process is shown to be an instability mechanism similar to that due to Craik (1977). The wave vorticity model is compared favourable with the Craik & Leibovich model for a range of surface wave conditions. A numerical model is constructed and characteristics of the Langmuir circulations, such as rate of growth and preferred cell size, are shown to depend on the value of a dimensionless 'Langmuir' number, La , defined in a similar way to that in Craik & Leibovich, to include a dependence on wind speed, turbulent viscosity and a combination of surface wave parameters. Small values of La, typically 0.01 to 0.05, causes a rapid growth (several minutes) of small cells. A notable feature in this case is the bifurcation of any larger cells present. For larger values of La, typically 0.1, a slower growth takes place and there is a tendency for the rejoining of smaller cells to form larger ones. The formulation of the model allows an interpretation, for all runs, in terms of either the wave vorticity or the Craik and Leibovich mechanisms.

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