Modification of wind-driven circulation and stratified spin-up at ocean fronts

A weakly nonlinear analytical theory along with two-dimensional, nonhydrostatic numerical simulations are used to study the adjustment of the Ekman transport and wind-driven secondary circulation in the presence of strong vertical vorticity and lateral density gradients typical of ocean fronts. The secondary circulation and fronts used in this study are generated by the application of wind-stress, varying sinusoidally in the direction perpendicular to the wind's orientation, to an initially quiescent, uniformly stratified, rotating fluid. When advection of the along-front momentum by the flow in the Ekman layer is retained in the momentum equations, the Ekman transport is found to vary inversely with the absolute vorticity rather than the planetary vorticity. Consequently, as vertical vorticity is generated during the spin-up of the fluid by the secondary circulation, the vertical vorticity feeds back on the Ekman pumping/suction, enhancing pumping and reducing suction. This feedback mechanism causes anticyclonic vorticity to grow rapidly, reducing the absolute vorticity to negative values in as short a time as several inertial periods. At the same time, the vorticity modified Ekman pumping depresses and tilts isopycnals, forming a bowl-shaped mixed layer flanked by outcropping isopycnals. These processes, characterizing the early stage of spin-up, were evident in numerical simulations scaled to the ocean.

Beyond this stage, the simulations expose the development of overturning cells with lateral length-scales smaller than the Rossby radius of deformation. These overturning cells come in two types (type I and II) distinguished by their formation mechanism. Type I overturning cells are mechanically driven by the vorticity modified Ekman pumping, whereas type II cells are driven by buoyancy twisting. Type I cells are characterized by a narrow zone of intense downwelling where the absolute vorticity is negative, trailed by a broader region of upwelling where the absolute vorticity is nearly zero and the density is well mixed. Type II cells, on the other hand, are trapped to outcropped isopycnals where the lateral density gradients are largest. The flow within these cells is not in a thermal wind balance. This imbalance causes overturning, inducing flow down the outcropped isopycnal.