The Galerkin method applied to convective instability problems

Bruce A. Finlayson
1968 Journal of Fluid Mechanics  
The Galerkin method is applied in a new way to problems of stationary and oscillatory convective instability. By retaining the time derivatives in the equations rather than assuming an exponential time-dependence, the exact solution is approximated by the solution to a set of ordinary differential equations in time. Computations are simplified because the stability of this set of equations can be determined without finding the detailed solution. Furthermore, both stationary and oscillatory
more » ... bility can be studied by means of the same trial functions. Previous studies which have treated only stationary instability by the Galerkin method can now be extended easily to include oscillatory instability. The method is illustrated for convective instability of a rotating fluid layer transferring heat.
doi:10.1017/s0022112068002454 fatcat:7nhvbuvb5neazdesfpujw6mdye