A spectral approach to thin jet flow

Steady and transient two-dimensional thin jet flow of a Newtonian fluid is examined numerically. The influence of inertia and gravity is emphasized. The fluid is assumed to emerge from a vertical channel, driven by a pressure gradient and/or gravity. The boundary layer equations are assumed for the thin film. In contrast to the commonly used depth-averaging solution method, the strong nonlinearities are preserved in the present formulation as the boundary layer equations are solved by expanding the flow field in terms of orthonormal shape functions in the transverse direction to the jet. It is found that the initial conditions strongly determine the stability of the film, which for all transient cases examined, were shown to be stable despite the presence of initial instabilities.