A model of the effects of horizontal density gradients on mixing processes in the oceanic surface layer

Abstract

A diurnal Eulerian model of the upper mixed layer incorporating the effects of horizontal density gradients is developed based on that of Janowitz and Kamykowski [1991] and is utilized to study the effects of wind‐driven cross‐isopycnal transport on mixing processes in the layer. Four runs of the model are conducted for a constant horizontal density gradient of 2.5 × 10−5 kg m−4 with wind directions at 0°, 90°, 180°, and 270° to this gradient. Two runs are conducted with half this density gradient and wind directions 90° to the left and right of the gradient and one run with no density gradient. In all cases the model is first run with a constant heat loss rate of 150 W m−2 through the sea surface for 11 hours to simulate nighttime cooling and to provide initial conditions for daytime runs. The model is then run for 24 hours with a constant wind speed of 7 m s−1 and a maximum solar radiation of 900 W m−2 during the first 13 hours of the 24‐hour simulation. The results show that the shallowest mixed layer occurs when the wind direction is 90° to the left of the density gradient and the deepest layer occurs with the wind direction 90° to the right of the gradient. After 24 hours, the ratio of the deepest to the shallowest mixed layer depth is 2.35 for the stronger gradient and 1.83 for the weaker gradient. These results are explained by the effect of vertical shear of the wind‐driven advection of horizontal density variations, which changes the vertical density gradient and can destabilize or stabilize the mixed layer. The results indicate that wind‐driven, cross‐isopycnal transport can have significant effects on mixing processes in the layer. Dimensionless parameters are developed to estimate the relative importance of cross‐isopycnal, wind‐driven transport on mixed layer properties.