A nonlinear instability burst in plane parallel flow
作者： L. M. Hocking , K. Stewartson , J. T. Stuart , S. N. Brown
DOI: 10.1017/S0022112072001326
关键词:
摘要: An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at Reynolds number R slightly greater than the critical value Rc for instability. After long time, t, consists of modulated wave whose amplitude A slowly varying function position and time. In an earlier paper (Stewartson & Stuart 1971) parabolic differential equation satisfied by two-dimensional disturbances was found; theory here extended to three dimensions. Although coefficients are coinples, start made elucidating properties its solutions assuming that these real. It then found numerically confirmed analytically that, finite (R-Rc)t, develops infinite peak centre. The possible relevance this work phenomenon transition discussed.
harvard.edu
sci-hub.se 参考文章(32)
M. Gaster, Growth of Disturbances in Both Space and Time Physics of Fluids. ,vol. 11, pp. 723- 727 ,(1968) , 10.1063/1.1691990
ERIK MOLLO-CHRISTENSEN, Physics of Turbulent Flow AIAA Journal. ,vol. 9, pp. 1217- 1228 ,(1971) , 10.2514/3.49933
J. Watson, On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow Journal of Fluid Mechanics. ,vol. 9, pp. 371- 389 ,(1960) , 10.1017/S0022112060001171
On the Nonlinear Response of a Marginally Unstable Plane Parallel Flow to a Two-Dimensional Disturbance Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 326, pp. 289- 313 ,(1972) , 10.1098/RSPA.1972.0010
D. L. T. Anderson, G. H. Derrick, Stability of Time‐Dependent Particlelike Solutions in Nonlinear Field Theories. II Journal of Mathematical Physics. ,vol. 11, pp. 1336- 1346 ,(1970) , 10.1063/1.1665265
On the Stability for Three-Dimensional Disturbances of Viscous Fluid Flow between Parallel Walls Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 142, pp. 621- 628 ,(1933) , 10.1098/RSPA.1933.0193
William O. Criminale, Leslie S. G. Kovasznay, The growth of localized disturbances in a laminar boundary layer Journal of Fluid Mechanics. ,vol. 14, pp. 59- 80 ,(1962) , 10.1017/S002211206200107X
Tsuguhiro Watanabe, A Nonlinear Theory of Two-Stream Instability Journal of the Physical Society of Japan. ,vol. 27, pp. 1341- 1350 ,(1969) , 10.1143/JPSJ.27.1341
H. Komoda, Nonlinear Development of Disturbance in a Laminar Boundary Layer Physics of Fluids. ,vol. 10, pp. S87- ,(1967) , 10.1063/1.1762512
Alan C. Newell, J. A. Whitehead, Finite bandwidth, finite amplitude convection Journal of Fluid Mechanics. ,vol. 38, pp. 279- 303 ,(1969) , 10.1017/S0022112069000176