Asymptotic Theory of Stability of a Viscous Fluid Jet Ejected along a Wall

Abstract

A linear and weakly nonlinear theory of stability of a laminar viscous fluid wall jet is considered. At large Reynolds numbers (calculated from the characteristic jet length) the undisturbed stationary flow is concentrated in a narrow region adjacent to the rigid surface. Nonstationary perturbations of this flow can be described by equations similar to the equations used in the theory of free interaction of a boundary layer. Such a description is made possible by introducing asymptotic order relations between the Reynolds number and the perturbation amplitudes and wavelengths. The set of solutions of the dispersion relation for the linear stability problem includes the eigenvalues of the phase velocities and wave numbers corresponding to the neutral and unstable perturbation modes. For finite fluctuation amplitudes, the evolution of the wave fields obeys the Korteweg-de Vries equations.