Abstract
Within the framework of the triple-deck theory, the linear stage of the development of three-dimensional disturbances in the Poiseuille-Couette flow was investigated. Numerical computations revealed “ripples” developing in the side direction in the initial phase of the linear stage. As in the case of two-dimensional disturbances, an increase in the relative velocity of the walls leads to the splitting of disturbances into two wave packets, of which the first grows faster and moves at a higher velocity. The disturbances propagate within a certain angle range.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Ya. Neiland, “Towards a Theory of Separation of the Laminar Boundary Layer in a Supersonic Stream,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 4, 53–58 (1969).
K. Stewartson and P. G. Williams, “Self-Induced Separation,” Proc. R. Soc. London, Ser. A 312(1509), 181–206 (1969).
A. F. Messiter, “Boundary-Layer Flow near the Trailing Edge of a Flat Plate,” SIAM J. Appl. Math. 18(1), 241–257 (1970).
V. I. Zhuk and O. S. Ryzhov, “Free Interaction of Near-Wall Layers with the Poiseuille Flow Core,” Dokl. Akad. Nauk SSSR 257, 55–59 (1981).
E. V. Bogdanova and O. S. Ryzhov, “On Oscillations Excited by a Harmonic Oscillator in the Poiseuille Flow,” Dokl. Akad. Nauk SSSR 257, 837–841 (1981).
I. V. Savenkov, “Features of the Linear Stage of Development of 3D Wave Packets in a Plane Poiseuille Flow,” Zh. Vychisl. Mat. Mat. Fiz. 49, 1271–1279 (2009) [Comput. Math. Math. Phys. 49, 1212–1220 (2009)].
F. T. Smith and S. J. Cowley, “On the Stability of Poiseuille-Couette Flow: A Bifurcation from Infinity,” J. Fluid Mech. 156, 83–100 (1985).
V. I. Zhuk and I. G. Protsenko, “Asymptotic Structure of Wave Disturbances in the Stability Theory of a Plane Couette-Poiseuille Flow,” Zh. Vychisl. Mat. Mat. Fiz. 45, 1060–1080 (2005) [Comput. Math. Math. Phys. 45, 1023–1042 (2005)].
I. V. Savenkov, “Features of Wave Packets in the Plane Poiseuille-Couette Flow,” Zh. Vychisl. Mat. Mat. Fiz. 48, 1274–1281 (2008) [Comput. Math. Math. Phys. 48, 1203–1209 (2008)].
F. T. Smith, “On the High Reynolds Number Theory of Laminar Flows,” IMA J. Appl. Math. 28, 207–281 (1982).
O. S. Ryzhov and E. D. Terent’ev, “Transient Regime Characterizing the Startup of a Vibrator in a Subsonic Boundary Layer on a Plate,” Prikl. Mat. Mekh. 50, 974–986 (1986).
O. S. Ryzhov and I. V. Savenkov, “Asymptotic Theory of a Wave Packet in on a Plate Boundary Layer,” Prikl. Mat. Mekh. 51, 820–828 (1987).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.V. Savenkov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 8, pp. 1471–1480.
Rights and permissions
About this article
Cite this article
Savenkov, I.V. Features of the linear stage of the development of 3D disturbances in the plane Poiseuille-Couette flow. Comput. Math. and Math. Phys. 50, 1399–1408 (2010). https://doi.org/10.1134/S0965542510080105
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542510080105