
21Vibrations and Stability at the Bulk and at the Interface
=
π+
R
a
a
3
2
(2.37)
that has its minimum at
equal to
=π≈R
27
657.51
a
4
(2.38)
The result is interpreted in such a way that when the Rayleigh number
reaches the critical value, the steady-state solution becomes unstable and the
convection cells emerge. Note that the linear analysis of the small perturba-
tion does not provide the solution for the cells; however, it indicates the con-
dition under which the perturbations grow. These growing perturbations
eventually emerge into the cells, which constitute a non-linear solution.
The Benard cells problem possesses features typical for ma ...