Abstract
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. G. Danilov and M. V. Makarova, “Asymptotic and numerical analysis of the flow around a plate with small periodic irregularities,” Russian J. of Math. Phys. 2 (1) (1994).
V. G. Danilov, V. P. Maslov, and K. A. Volosov, Mathematical Modeling of Heat and Mass Transfer Processes (Kluwer Academic Publishers, Dordrecht, 1995).
V. G. Danilov and R. K. Gaydukov, “Oscillations in classical boundary layer for flow with double-deck boundary layers structure,” in Proceedings of International Conference “Days on Diffraction,” May 27–31 2013, St. Petersburg (IEEE, 2013), pp. 28–31.
V. G. Danilov and R. K. Gaydukov, “Vortexes in the Prandtl boundary layer induced by irregularities on a plate,” Russian J. Math. Phys. 22 (2), 161–173 (2015).
R. Yapalparvi, “Double-deck structure revisited,” European Journal of Mechanics B/Fluids 31, 53–70 (2012).
F. T. Smith and P. W. Duck, “Separation of jets or thermal boundary-layers from a wall,” Q. J. Mech. Appl. Math. 30, 143–156 (1977).
J. Mauss, A. Achiq, and S. Saintlos, “Sur l’analyse conduisant ála théorie de la triple couche,” C. R. Acad. Sci. Paris, t 315, Série II, 1611–1614 (1992).
J. Mauss, “Asymptotic modelling for separating boundary layers,” Lecture Notes in Physics 442, 239–254 (1995).
O. S. Ryzhov and E. D. Terent’ev, “A nonstationary boundary layer with self induced pressure,” Appl. Math. Mech 41 (6), 1007–1023 (1977).
F. T. Smith, “Laminar flow over a small hump on a flat plate,” J. Fluid Mech. 57 (4) (1973).
K. Stewartson, “Multistructured boundary layers on flat plates and related bodies,” Adv. Appl. Mech. 14, 145–239 (1974).
L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987).
V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin–New York, 1989).
V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equation (Dover Publication Inc., New York, 1989).
H. Schlichting and K. Gersten, Boundary Layer Theory (Springer-Verlag, Berlin–New York, 2000).
M. Van Dyke, An Album of Fluid Motion (Parabolic Press, 1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article was submitted by the authors for the English version of the journal.
Rights and permissions
About this article
Cite this article
Danilov, V.G., Gaydukov, R.K. Double-deck structure of the boundary layer in problems of flow around localized perturbations on a plate. Math Notes 98, 561–571 (2015). https://doi.org/10.1134/S0001434615090242
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434615090242