| Abstract: | A new approach to the investigation of the nonlinear development of disturbances, based on the theory of invariant manifolds, is outlined. A method of obtaining projections of the Navier-Stokes equations on finite-dimensional invariant manifolds is proposed. The behavior of the disturbances is finally described by a system of ordinary differential equations with right sides in the form of power series in the amplitudes. It is an important property of the method that these series are convergent. A two-dimensional invariant projection is calculated numerically for plane Poiseuille flow. As a result, it is possible to clarify the nature of the change from subcritical to supercritical bifurcation and investigate new bifurcations of periodic flow regimes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 9–15, January–February, 1990.The author is grateful to A. Zharilkasinov for carrying out the numerical calculations. |
