Numerical Modelling of Langmuir Circulation and Its Application

Abstract

Nonlinear momentum and vorticity equations incorporating the interaction of surface gravity waves with a drift current were derived in previous studies of Langmuir circulation (Leibovich, 1977). The length, time, and velocity scaling of this set of equations is shown here, for oceanic conditions, to depend only upon the wind speed when suitable empirical formulations are used. These equations together with the continuity equation are solved numerically by use of the semi-spectral method (Orszag and Israeli, 1975) by representing the x-components (parallel to the wind) of velocity (u) and vorticity and the streamfunction (in the y-z plane) by truncated Fourier series. Also, a no-slip condition is used at the bottom boundary to allow the development of a quasi-steady state. Numerical results are obtained for Langmuir numbers (an inverse Reynolds number) of 0.1 and 0.01 with scaled depths of 1, 2, and 4. Two initial conditions are imposed: one from total rest and the other from an initial horizontally uniform velocity parallel to the wind. The wind stress starts abruptly and remains constant. Numerical results indicate that the stream function shows the cellular structure and profiles of the mean velocity u show high shear in the upper and lower layers of each cell. The salient features of Langmuir cells are reproduced and quantitative comparisons show good agreement between previous field measurements and model results using the wind velocity scaling (Faller and Caponi, 1978).