Spin-up of a liquid with a density maximum in a cylinder

A study is made of the spin-up of a viscous non-Boussinesq fluid in a vertically mounted cylinder. The density (ρ) of the fluid becomes maximum at temperature Tm, and a quadratic density–temperature relation is used. The fluid is stratified by imposing a vertical temperature contrast, with the temperature at the bottom endwall disk being Tm. Comprehensive numerical solutions to the time-dependent Navier–Stokes equations are acquired. Due to the vertically non-uniform stratification, spin-up proceeds faster near the bottom endwall than near the top endwall. The meridional circulation is more intense near the bottom endwall. Detailed descriptions of evolutions of both azimuthal and meridional flows are given. Major differences in dynamic characteristics are illustrated between a homogeneous fluid, a Boussinesq fluid, and the present non-Boussinesq fluid which has a density maximum.