On the Nonlinear Response of a Marginally Unstable Plane Parallel Flow to a Two-Dimensional Disturbance

摘要: The differential equation governing the nonlinear evolution of an initial centred infinitesimal disturbance to a marginally unstable plane parallel flow was obtained by Stewartson & Stuart (1971) and some its properties elucidated Hocking, (1972). Of especial interest is final localized burst solution which occurs when all coefficients are real first Landau constant positive. In Poiseuille flow, however, standard example these complex in present paper analytic numerical study made they permitted take general values. It found that if part $\delta \_{\text{r}}$ positive it possible have either or remains finite for time depending on values other coefficients. addition can two different structures. If \_{\text{r}}<$< 0 solutions remain but amplitude oscillation does not tend limit imaginary _{\text{i}}$ large enough. For particular skewed disturbances only inclined main stream at angle exceeding about 56$^{\circ}$.