Transition to chaos in doubly-diffusive convection

Two-dimensional thermosolutal convection in a horizontal layer of fluid heated from below is investigated analytically in the Boussinesq approximation, summarizing the results of Moore et al. (1983) and Knobloch et al. (1984). The nondimensional convection equations with their boundary conditions are presented and solved numerically with a second-order finite-difference scheme, treating the nonlinear terms explicitly, representing the diffusion terms by a Dufort-Frankel scheme, and solving the associated Poisson equation (linking the stream function with the vorticity) by Fourier decomposition and tridiagonal elimination. The results are presented graphically; the transition to chaos is characterized; and the theoretical implications are explored.