No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
A non-perturbative approach to spatial instability of weakly non-parallel shear flows
4.J. A. Ross, F. H. Barnes, J. G. Burns, and M. A. S. Ross, “The flat plate boundary layer. Part 3. Comparison of theory with experiment,” J. Fluid Mech. 43(04), 819–832 (1970).
5.Y. S. Kachanov and A. Michalke, “Three-dimensinoal instability of flat-plate bounday layers: Theory and experiment,” Eur. J. Mech. B-Fluid. 13(4), 401–422 (1994).
6.Y. S. Kachanov and T. G. Obolentseva, “Development of three-dimensional disturbances in the Blasius boundary layer 3. Nonparallism effects,” Thermophys. Aeromech. 5(3), 331–338 (1998).
9.M. Bouthier, “Stabilite lineaire des ecoulements presque paralleles,” J. Mec. 11, 599–621 (1972).
17.C. C. Lin, “On the stability of two-dimensional parallel flows,” Q. J. Mech. Appl. Maths 3, 117–142 (1946).
19.R. J. Bodonyi and F. T. Smith, “The upper branch stability of the Blasius boundary layer, including non-parallel flow effects,” Proc. R. Soc. London, Ser. A 375(1760), 65–92 (1981).
21.M. R. Turner and P. W. Hammerton, “Asymptotic receptivity analysis and the parabolized stability equation: A combined approach to boundary layer transition,” J. Fluid Mech. 562, 355–381 (2006).
22.Z. F. Huang, H. Zhou, and J. S. Luo, “Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis,” Sci. China, Ser. G 48, 626–640 (2005).
23.Z. F. Huang, W. Cao, and H. Zhou, “The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode,” Sci. China, Ser. G 48, 614–625 (2005).
26.Y. S. Kachanov and T. G. Obolentseva, “Development of three-dimensinoal disturbances in the Blasius bounday layers 1. Wave-trains,” Thermophys. Aeromech. 3(3), 225–243 (1996).
27.Y. S. Kachanov and T. G. Obolentseva, “Development of three-dimensinoal disturbances in the Blasius bounday layers 2. Stability characteristics,” Thermophys. Aeromech. 4(4), 373–384 (1997).
29.X. Wu and M. Dong, “On continuous spectra of the Orr-Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances,” J. Fluid Mech. 732, 616–659 (2013).
30.A. Butler and X. Wu, “Non-parallel-flow effects on stationary crossflow vortices at their genesis,” in Proc. IUTAM Symposium on Laminar-Turbulent Transition, Rio de Jeneiro, Brazil, edited by M. Medeiros (Elsevier, 2015 , in press).
Article metrics loading...
Boundary-layer instability is influenced by non-parallel-flow effects, that is, the streamwise variation of the mean flow not only modifies directly the growth rate but also distorts the shape (i.e., the transverse distribution) of the disturbance, thereby affecting the growth rate indirectly. In this paper, we present a simple but effective local approach to spatial instability of three-dimensional boundary layers, which takes into account both direct and indirect effects of non-parallelism. Unlike existing WKB/multi-scale type of methods, the present approach is non-perturbative in which non-parallelism does not need to be a higher-order correction to the leading-order prediction by the parallel-flow approximation. The non-parallel-flow effects are accounted for by expanding the local mean flow and the shape function as Taylor series, and this leads to a sequence of extended eigenvalue problems, depending on the order of truncation of the Taylor series. These eigenvalue problems can be solved effectively by standard numerical methods. In the case of the Blasius boundary layer, the predictions are verified and confirmed by direct numerical simulation results as well as by the non-parallel theory of Gaster. The non-parallel-flow effects on the eigenvalues, eigenfunctions, and neutral curves for planar and oblique Tollmien-Schlichting (T-S) waves are discussed. The distortion of the eigenfunction is found to have a significant effect, which may be stabilizing or destabilizing depending on the ranges of the Reynolds number and frequency.
Full text loading...
Most read this month