Large-eddy Simulation of Ekman Layer Instabilities in the Ocean Mixed Layer: Comparison with Theory

Coherent roll structures are often produced in large-eddy simulations (LES) of the wind- and wave-forced ocean boundary layer. In many cases, these circulations can be attributed to wave interactions leading to Langmuir circulation. However in frontal zones, strong coherent rolls are simulated that do not depend on surface wave forcing. Here we test the hypothesis that these rolls are produced by an Ekman instability that results from wind-generated shear. Simulations using a LES model are conducted using a basic Ekman spiral initial condition and compared with direct-numerical simulations (DNS) for cases where linear stability analysis suggests growth of shear instability. Initial conditions are applied in a DNS configuration with Reynolds number of 500. In both cases, roll structures with horizontal scales 5-6 times the mixed layer depth are produced with orientation roughly 20 degrees from the Ekman surface velocity, agreeing with analytical solutions.