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

Abstract

This work examines the stability of surface frontogenesis in the presence of a horizontal density gradient and an ageostrophic current. We pose an initial 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 adjustment process is simulated using a fully nonlinear pseudo spectral numerical calculation in a 10 km X 30 m range and depth domain. We allow the evolution of the surface current jet but do not permit its variation in the y direction (perpendicular to the computational domain). A number of simulations are performed for a wide range of density differences and jet strengths. Surface frontogenesis and a tendency toward geostrophic adjustment of the initially ageostrophic fields do not always exhibit a smooth subsurface circulation accompanying the bunching of the surface isopycnals. Instead, a vortex is sometimes shed from the vicinity of the evolving front, and the isopycnals are distorted by this smaller-scale vortical flow. To determine the source of the secondary symmetric baroclinic instability, the acceleration potential of the individual terms in the vorticity equation is calculated. The instability is caused by the vertical shear in the along-front jet, which is intensified by the advection and vortex-tilting processes during the frontogenesis. Although this vortex is left behind by the propagating hydraulic jump, it subsequently matures into a secondary hydraulic jump on its own. We found that in marginally unstable cases an increase in the kinematic viscosity can suppress its occurrence. Finally, we show that the unstable 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. Copyright 1999 by the American Geophysical Union.