Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent.
Baghdasarian, M., Pacheco-Vega, A., Pacheco, J. R., & Verzicco, R. (2014). Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes. Physics of fluids, 26(9), -. . https://doi.org/10.1063/1.4895435