Theoretical and observational study of Langmuir circulation

Abstract

Craik (1977) showed from the theory developed by Leibovich (1977) that cellular roll motion similar to that found in Langmuir cells can develop as an instability due to the interaction of surface waves and currents. Solutions are obtained here as an initial value problem to the Craik-Leibovich equations using a semi-spectral numerical model for cases with finite fluid depth, constant density, and horizontally uniform Stokes drift. Two values of the Langmuir number (La) are used, one to represent oceanic conditions and the other for laboratory scales. Steady states are nearly reached in all runs. Comparisons with historical field and laboratory data show good agreement with the model results. A linear stability analysis made using a subset of the semi-spectral model equations shows that instability occurs for values of La as large as 1.0. However, as depth decreases, the critical value of La also decreases. The results of a recent field study of Langmuir cells and small scale circulation are presented. Dye, computer cards, and drifters were used as surface or near surface tracers of water motion and were photographed at five minute intervals for three hours on three different days. The length, direction and distance between card rows, which form at the convergences of the Langmuir cells were measured. Relationships between mixed layer depth, wind speed, and cell width, determined from the experiment are examined and compared to historical observations. Large scale modulation of the down-wind surface water velocities at the convergences occurred when the wind speed and direction were relatively constant. Dispersion of the drifters was negligible in the cross-wind direction under constant wind conditions. Horizontal eddy viscosity, computed from the dispersion of the drifters, compared favorably with the observations collected by Okubo (1971), only when the wind direction was turning rapidly and cells were not evident.