Classical Boussinesq Approximation Research Articles

A numerical study of the applicability of the Boussinesq approximation for a fluid‐saturated porous medium

AbstractThe regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid‐saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water‐saturated porous region.

Note on cellular convection with nonisotropic eddies

According to Krueger and Fritz (1961). one of the outstanding features calling for explanation in the cellular cloud patterns revealed by satellites is that the diameter-to-depth ratio i s around 30, instead of about 3 as predicted by classical theory and verified by laboratory experiments.” This call for explanation in the introductory sentence of a short communication by Priestley (1962) is as urgent today as 21 years ago. He advocated and Ray (1965) calculated the influence of anisotropic eddy dilfusion as a possible solution to the problem of cell flatness. Using the classical Boussinesq approximation to describe Rayleigh-Benard convection and introducing turbulent horizontal heat and momentum dilfusion coefficients of about 100 times the vertical value, results in cell aspect ratios of the required magnitude. This was confirmed recently by Sheu et al. (1980) making eddy anisotropy a major candidate for explanation of the dilference between observation and theory (also Agee and Mitchell, 1977). DOI: 10.1111/j.1600-0870.1984.tb00225.x