Mixing in thermally stratified nonlinear spin-up with sources and sinks

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 address how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. Measurements of efficiency of mixing are based on the variance of temperature and explained in terms of the potential energy available. 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 lacking.Comment: Submitted to Physics of Fluids, 9 figure

Mixing in Thermally Stratified Nonlinear Spin-up Flows with Uniform Boundary Fluxes

Spin-up flows, which result when fluids experience an impulsive increase in their rotation rate, are relevant to large-scale geophysical fluid motions. Mixing of temperature, pollution and nutrition in such flows are important aspects of our climate change, and ocean-atmospheric circulations. Therefore, the goal of this study is to quantify the mixing efficiency of cylindrical spin-up flows under four sets of thermal boundary conditions using the variance of temperature. The interpretation of the results are based on the concept of available and background potential energies. Finite differences in conjunction with the fractional step method is used to numerically solve the Navier-Stokes equations. The imposed boundary conditions on the horizontal walls include isothermal, adiabatic and a combination of both. From the analysis of the results it was found that adiabatic condition at the top of the cylinder, and isothermal at the bottom enhances the mixing efficiency of the fluid after 130 rotations