Curved density fronts: Cyclogeostrophic adjustment and frontogenesis

Curvature can play a significant role in the dynamics of density fronts at small scales and in low-latitude regions of the ocean. Fronts can be displaced from balance by rapid forcing and undergo an adjustment toward a more stable state or be strained and sharpened by surrounding flow in a process known as frontogenesis. This study investigates the role of curvature in adjustment and frontogenesis using the idealized configuration of an axisymmetric eddy and associated circular front. As a result of the curvature, the balanced state of this system is not geostrophic balance, where pressure and Coriolis forces exactly balance, but cyclogeostrophic balance, where pressure and Coriolis forces combine to supply a net inwards centripetal force on fluid parcels. The parameter range for which cyclogeostrophically balanced states exist for a given unbalanced initial condition is determined. This parameter range is smaller for anticyclonic fronts (i.e., fronts curved around a warm core), which have larger angular velocities than comparable straight fronts, implying they are more likely to break down during adjustment. The reverse is true for cyclonic fronts. A model for the sharpening of a curved front in a background strain flow, analogous to the Hoskins and Bretherton (1972) model for a straight front, is developed. Relative to a straight front subject to the same strain rate, vertical velocities are weaker for an anticyclonic front and stronger for a cyclonic front. Anticyclonic fronts collapse to a near discontinuity during frontogenesis far more rapidly than cyclonic fronts for the same strain rate.