ESS228
Prof. Jin-Yi Yu
Purpose of Boussinesq Approximation
•This approximation states that density differences are
sufficiently small to be
neglected, except where they appear in terms multiplied by g, the acceleration due to gravity (i.e., buoyancy).
•In the Boussinesq approximation, which is appropriate
for an almost- incompressible
fluid, it assumed that variations of density are small, so that in the intertial terms, and in the continuity equation,
we may substitute r by r0, a constant. However, even weak density variations are
important in buoyancy,
and so we retain variations in r in
the buoyancy term in the vertical
equation of motion.
•Sound
waves are impossible/neglected when the Boussinesq approximation is used, because sound waves move via
density variations.
•Boussinesq approximation is for the problems that the
variations of temperature
as well as the variations of density are small. In these cases, the variations in volume expansion due to temperature
gradients will also small. For
these case, Boussinesq approximation can simplify the problems and save computational time.