Symmetric baroclinic instability during frontogenesis with horizontal density gradients and ageostrophic vertical shears

This work examines the stability of surface frontogenesis in the presence o f a horizontal density gradient and an ageostrophic current. We pose an ini tial value problem, in which two homogeneous bodies of water with different densities are separated by a horizontal transition region for the density. A surface current jet flows along the density front, and the geostrophic a djustment process is simulated using a fully nonlinear pseudo spectral nume rical calculation in a 10 km x 30 m range and depth domain. We allow the ev olution of the surface current jet but do not permit its variation in the y direction (perpendicular to the computational domain). A number of simulat ions are performed for a wide range of density differences and jet strength s. Surface frontogenesis and a tendency toward geostrophic adjustment of th e initially ageostrophic fields do not always exhibit a smooth subsurface c irculation accompanying the bunching of the surface isopycnals. Instead, a vortex is sometimes shed from the vicinity of the evolving front, and the i sopycnals are distorted by this smaller-scale vortical flow. To determine t he source of the secondary symmetric baroclinic instability, the accelerati on potential of the individual terms in the vorticity equation is calculate d. The instability is caused by the vertical shear in the along-front jet, which is intensified by the advection and vortex-tilting processes during t he frontogenesis. Although this vortex is left behind by the propagating hy draulic jump, it subsequently matures into a secondary hydraulic jump on it s own. We found that in marginally unstable cases an increase in the kinema tic viscosity can suppress its occurrence. Finally, we show that the unstab le vortex is separate and distinct from the captured turbulent rotor which is thought to be locally trapped at a location just behind the propagating front.