On the stability of free convection flow along a heated vertical plate

A nonlinear analysis of the stability of a flow along a flat plate (Blasius) was applied to the free-convection flow along a heated vertical plate. Together with amplified linear oscillations of the Tollmien-Schlichting type, amplified three-dimensional oscillations were investigated. The superposition of these two linear oscillations shows the characteristic M-shaped profile in the main-stream direction. The numerical treatment of the quadratic nonlinear terms occurring in a perturbation series expansion shows a dominant multiple system of longitudinal vortices of the Taylor-Goertler type. Its amplification rate is the sum of the rates of the two linear oscillations. Among the nonlinear components dependent upon the mainstream direction, the interaction constituents for the linear perturbations are also dominant.