| Abstract: | 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.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 2, pp. 19–26, March–April, 1981. |
