Multiple steady states of buoyancy induced flow in cold water and their stability

The physical background and the literature related to buoyancy-induced flows are reviewed. An accurate representation, based upon experimental data, of the motion-causing buoyancy force, in the vicinity of maximum density in pure water at low temperatures, is used. Using the representation, numerically a model for the laminar, boundary layer flow arising from natural convection adjacent to a vertical isothermal flat surface submerged in quiescent cold water is studied. The results demonstrate for the first time the existence of multiple steady-state solutions in a natural convection flow. The existence of these new multiple steady-state solutions led to an investigation of their stability. Three real eigenvalue and eigenvector pairs corresponding to the new steady-state-solutions were found. Each of these eigenvalues changes its algebraic sign at a particular limit point (point of vertical tangency, nose, knee) in the bifurcation diagrams.