Influence of external flow field on the equilibrium state of quasi-geostrophic point vortices

Abstract

The influence of external flow field on the statistical equilibrium state of quasi-geostrophic point vortices (vortex cloud) is investigated numerically. The numerical computations are performed using the fast special-purpose computer for molecular dynamics simulations, MDGRAPE-3. The equilibrium state in otherwise quiescent fluid is axisymmetric, whose radial distribution depends on both the vertical distribution of vortices P(z) and the total energy of the vortex system E. At a certain critical energy value E _c , the number of microscopic state with a given angular momentum attains its maximum (zero-inverse temperature state), where the radial distribution is Gaussian at any vertical height. When the energy is smaller (E < E _c : positive temperature), the radial distribution becomes flatter than the Gaussian. In contrast, if the energy is higher (E > E _c : negative temperature), the radial distribution becomes sharper showing tighter concentration near the axis of symmetry. If an equilibrium vortex cloud of positive temperature is immersed in the horizontal strain field U _e = ey, V _e = ex, the vortex distribution is stretched in the y-direction, and the azimuthally averaged radial distribution becomes Gaussian-like. Similarly, when the equilibrium state of positive temperature is immersed in the vertical shear field U _τ = τz, V _τ = 0, the vortex cloud is tilted in the y-direction, and the radial distribution becomes Gaussian-like. These findings explain how the internal vorticity distributions inside interacting vortex clouds of positive temperature change to be nearly zero-inverse temperature state.

Keywords:

• Quasi-geostrophic point vortices
• Equilibrium states
• Horizontal strain
• Vertical shear

Acknowledgements

We are grateful for the support of Dr Matsubara (RIKEN) throughout this work, and thank RIKEN Integrated Cluster of Clusters (RICC) for their computational resources.