Effects of convection and diffusion in the viscous Lamb dipole

We present a numerical study of the viscous Lamb dipole in the Reynolds number range $125 \le Re \le 1000$. The effects of convection and diffusion are examined by comparing solutions of the Navier-Stokes equations (NSE) and diffusion equation (DE) with the inviscid Lamb dipole as the initial condition. The results show that for a given Reynolds number, the vortex core size, shape, and maximum vorticity are diffusion-dominated features. However, the total circulation is affected by convection; at low $Re$, convection in the NSE inhibits circulation decay in comparison to the DE, while it enhances circulation decay at high $Re$. The lateral separation of the vortex cores plays a key role in this transition.