The Halting Effect of Baroclinicity in Vortex Merging

Abstract

We study the quasigeostrophic merging dynamics of axisymmetric baroclinic vortices to understand how baroclinicity affects merging rates and the development of the nonlinear cascade of enstrophy. The initial vortices are taken to simulate closely the horizontal and vertical structure of Gulf Stream rings. A quasigeostrophic model is set with a horizontal resolution of 9 km and 6 vertical levels to resolve the mean stratification of the Gulf Stream region. The results show that the baroclinic merging is slower than the purely barotropic process. The merging is shown to occur in two phases: the first, which produces clove-shaped vortices and diffusive mixing of vorticity contours; and the second, which consists of the sliding of the remaining vorticity cores with a second diffusive mixing of the internal vorticity field. Comparison among Nof, Cushman–Roisin, Polvani et al., and Dewar and Killworth merging events indicates a substantial agreement in the kinematics of the process. Parameter sensitivity experiments show that the decrease of the baroclinicity parameter of the system, Γ2, [defined as Γ2 = (D2f02)/(N02H2)], increases the speed of merging while its increase slows down the merging. However, the halting effect of baroclinicity (large Γ2 or small Rossby radii of deformation) reaches a saturation level where the merging becomes insensitive to larger Γ2 values. Furthermore, we show that a regime of small Γ2 exists at which the merged baroclinic vortex is unstable (metastable) and breaks again into two new vortices. Thus, in the baroclinic case the range of Γ2 determines the stability of the merged vortex. We analyze these results by local energy and vorticity balances, showing that the horizontal divergence of pressure work term [∇·(pv)] and the relative-vorticity advection term (v·∇∇2ψ) trigger the merging during the first phase. Due to this horizontal redistribution process, a net kinetic to gravitational energy conversion occurs via buoyancy work in the region external to the cores of the vortices. The second phase of merging is dominated by a direct baroclinic conversion of available gravitational energy into kinetic energy, which in turn triggers a horizontal energy redistribution producing the final fusion of the vortex centers. This energy and vorticity analysis supports the hypothesis that merging is an internal mixing process triggered by a horizontal redistribution of kinetic energy.