Laminar and Oscillatory Convection of a Fluid in a Closed Area with Lateral Heating

Results are presented from numerical parametric calculations based on a finite-difference solution of two-dimensional Navier–Stokes equations for a viscous incompressible fluid in a closed square region heated from the side. Gravitational convection is modeled for a wide range of defining dimensionless parameters: Grashof number 0 < Gr < {10^8}, Prandtl number 1{{0}^{ - 2}} < Pr < {10^2}, concentrational Grashof number 0 < G{{r}₂} < {10^8}, and Schmidt number 1{{0}^{ - 2}} < Sc < {10^2}. Results from modeling show the nonmonotonic nature of the dependence of the vertical stratification in temperature and concentration on the Grashof numbers, along with dynamics of the formation of steady-state oscillatory convective flows of a viscous liquid. For intense laminar convection, there is a narrow range of Grashof numbers that depends non-linearly on the Prandtl number. In this range, the steady convective flow has an ordered oscillatory periodic pattern caused by metastable changes in the stable state of secondary macro-vortices on the heated and cooled boundaries, and their subsequent movement along the closed boundary layer. When the Grashof numbers are raised even more, the periodic convective flow regime becomes a chaotic oscillatory and then turbulent regime.