Quasi-two-dimensional properties of a single shallow-water vortex with high initial Reynolds numbers

Abstract

The evolution and dynamics of a shallow-water vortex system with high initial Reynolds numbers are investigated experimentally without background rotation. A single vortex is generated by rotating a water mass at the centre of an experimental tank using a bottomless cylinder with internal sectors. The surface velocity field is observed via particle image velocimetry. The experimentally observed vorticity fields indicate that strong shallowness (the ratio of the cylinder diameter to the water depth) and high Reynolds number contribute to the formation of large-scale coherent structures in the form of a tripolar vortex system. The shallow-water vortices with high initial Reynolds numbers experience the transition from turbulent to laminar regimes in their decay process. The proposed first-order vortex decay model predicts that a shallow-water vortex decays as t−1 in the initial turbulent stage and as e−t in the later laminar stage due to horizontal diffusion and bottom friction. The estimated transition time scale from the turbulent to laminar stage increases with initial vortex Reynolds number and with shallowness. By taking the vortex expansion into consideration, the second-order vortex decay model is also presented. The azimuthally ensemble-averaged data elucidate effects of the vortex instabilities and of turbulent energy transfer on the formation of large-scale coherent flow structures. Normal mode analysis of the vortex systems is conducted to study the effect of shallowness and Reynolds number on the generation of two-dimensional large-scale coherent structures. The results show that the perturbation wavenumber of mode 2 is the fastest-growing instability in shallow-water conditions, and its effect depends on initial Reynolds number and shallowness.