Vortex Merger in Shallow Water Model

Abstract

An inviscid, nonlinear shallow water model is applied to study the formation of filaments and merging of potential vorticity (PV, π). We confirm that misalignment of vorticity with the streamlines is crucial to merger. Flow creates positive PV tendency (πt) on the lee side of π ridge, which increases the angle between streamlines and PV contours and the efficiency of vorticity transport along the parallel but oppositive direction in the positive quadrants of πt. So, the vortices move closer while rotating around each other. Filamentation starts as weak vorticity shatters from the outer edge of vortex core. The filament grows and rotates around the cores, but shows little effects to positive PV advection or vortex merging in the inner core, evidenced by the steady core area integrated PV trends. Consecutive PV transfer from lower to higher interval levels are observed during merger process while elongated filamentation is dissolving into the lower level PV regime. The vortices never merge when negative πt prevails between two vortices. Distance between the vortex cores show direct correspondence to positive πt between them. Hence, the advance of positive πt provides a simple mechanism of merging. The Rossby radius of deformation (LD) is confirmed to be another strong indicator for vortex pair merger where LD comparable or smaller than the initial vortex core separation length scale makes merger more likely due to geostrophic adjustment. The Rossby number (Ro) affected the overall flow interaction speed speed when LD is fixed.

Challenges and Progress in Computational Geophysical Fluid Dynamics in Recent Decades

“…The filaments become long, thin strips around the center (Figure 12f at t = 120 s). The vorticities are still distinguishable at the end of integration, t = 130 s and total kinetic energy, mass, and PV remain as initial values (Sun and Oh 2022) [62].…”

“…2.4.7. Vortices Merge (Sun and Oh 2022) [62] The domain consists of 450 × 450 grids, with ∆x = ∆y = 0.025 m. Following Waugh (1992) [63] and Oh (2007) [42], we set g = 1 m s −2 , and the initial surface perturbation is…”

An Efficient Forward Semi-Lagrangian Model

“…The characteristic-based Lagrangian models have been successfully applied to simulate the vortex merging, hydraulic jumps, and shear flows in the shallow water equations (Toro 1999, Wang and Yeh 2005, Oh 2007, and others) with CFL 1, their results are quite accurate compared with the high-order finite volume models (Sun 2011, Sun andOh 2022), but the former requires tremendous computing time. They are also difficult to apply to multi-dimensional flows.…”