Multiple solutions in fluid dynamics

Abstract

The principle of multiple solutions of the Navier-Stokes and energy equations discussed in this paper is not directed at any particular problems in fluid dynamics and heat transfer, or at any specific applications. The non-uniqueness principle states that the Reynolds number, above its critical value, is insufficient to uniquely determine a flow field for a given geometry, or for similar geometries. It is a generic principle for all fluid flows and its transportation properties, but is not well known. It compliments the current popular bifurcation theories by the fact that multiple solutions can exist on each stable bifurcation branch.