Accuracy of the Boussinesq approximation for a incompressible fluidстатья
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Дата последнего поиска статьи во внешних источниках: 4 сентября 2018 г.
Аннотация:The corrections of first order to the eigenvalues and critical Rayleigh numbers obtained in the Boussinesq approximation are determined for convection in a fluid with zero compressibility. The ratio of the equilibrium difference of the densities to a mean density of the fluid is taken as the small parameter. The corrections are found by the methods of perturbation theory for self-adjoint operators. It is shown that in the class of problems with symmetry with respect to a horizontal plane the first-order corrections vanish. The restrictions on the system needed if the Boussinesq approximation is to be meaningful in the problem of the occurrence of convective instability are established.