Anyone knows what does it mean by boussinesq approximations? Also is a flow still laminar at high Rayleigh's number of 1000000? Thank you.

A broad range of variable density flows have small density variations that can be modeled using a Boussinesq approximation. In the Boussinesq approximation density variations are assumed to be sufficiently small so that the density variation can be ignored in the momentum equation. The equations are only coupled through a gravitational forcing term.

From "A second-order projection method for variable-density flows" by John B. Bell and Daniel L. Marcus.

Kim

1) check any undergraduate fluid mechanics book.

2) depends on the problem.

Refer to above two comments. I think that their comments are perfect.

Adding some comments.

1. Boussinesq approximation : Rho = Rho)ref * (1 - alpha * (Tref-T)), where alpha means thermal expansion coefficient.

2. In general, natural convection of Ra=1000000 can be treated as laminar flow, especially for the natural convection in the (rectangular) cavity.

Sincerely, Jinwook