Application of Arnoldi method to boundary layer instability

doi:10.1088/1674-1056/24/12/124701

Abstract

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien-Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘angerous' in secondary instability.

Keywords: Arnildi method linear stability theory Floquet theory secondary instability

Received: 29 May 2015
Revised: 20 July 2015
Accepted manuscript online:

PACS:	47.20.Ib	(Instability of boundary layers; separation)
	47.20.Lz	(Secondary instabilities)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11202147, 11332007, 11172203, and 91216111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032120007).

Corresponding Authors: Zhang Yong-Ming
E-mail: ymzh@tju.edu.cn

Cite this article:

Zhang Yong-Ming (张永明), Luo Ji-Sheng (罗纪生) Application of Arnoldi method to boundary layer instability 2015 Chin. Phys. B 24 124701

[1]	Zhang Y, Zaki T, Sherwin S and Wu X 2011 6th AIAA Theoretical Fluid Mechanics Conference, June 27-30, 2011, Hawaii, USA, AIAA 2011
[2]	Zhou H and Zhao G F 2004 Hydrodynamic instability (Beijing: National Defense Industry Press) p. 147 (in Chinese)
[3]	Klebanoff P 1971 Bull. Am. Phys. Soc. 10 1323
[4]	Suder K L, O'Brien J E and Reshotko E 1998 NASA Tech. Mem. (Technical Report) 100913
[5]	Kendall J M 1990 AIAA Paper 85-1695
[6]	Roach P E and Brierley D H 1992 Numerical Simulation of Unsteady Flows and Transition to Turbulence (Cambridge: Cambridge University Press) p. 319
[7]	Westin K J A, Boiko A V, Klingmann B G B, Kozlov V V and Alfredsson P H 1994 J. Fluid Mech. 281 193
[8]	Matsubara M and Alfredsson P H 2001 J. Fluid Mech. 430 149
[9]	Theofilis V 2011 Ann. Rev. Fluid Mech. 43 319
[10]	Andersson P, Brandt L, Bottaro A and Henningson D S 2001 J. Fluid Mech. 428 29
[11]	Ricco P, Luo J and Wu X 2011 J. Fluid Mech. 677 1
[12]	Wang F Q, Zhang H and M X K 2012 Chin. Phys. B 21 020505
[13]	Zhu H X, Wang T T, Gao J S, Li S, Sun Y J and Liu G L 2014 Chin. Phys. Lett. 31 030503
[14]	Liu Y, Zaki T A and Durbin P A 2008 J. Fluid Mech. 604 199
[15]	Vaughan N J and Zaki T A 2011 J. Fluid Mech. 681 116
[16]	Ma D J, Sun D J and Yin X Y 2007 Chin. J. Comput. Phys. 24 7 (in Chinese)
[17]	Barkeley D, Blackburn H M and Sherwin S J 2008 Int. J. Numer. Meth. Fluids 57 1435
[18]	Blackburn H M, Barkeley D and Sherwin S J 2008 J. Fluid Mech. 603 271
[19]	Merle X, Alizard F and Robinet J C 2010 Computers & Fluids 39 911
[20]	Anderson E, Dongarra J and Ostrouchov S 1991 Implementation guide for LAPACK, UT CS-91-138, August 1991
[21]	Lehoucq R B, Sorensen D C and Yang C 1998 ARPACK user's guide: solution of large scale eigenvalue problem by implicitly restarted Amoldi method, Philadelphia, SIAM
[22]	Wesin K J A, Bakchinov A A, Kozlov V V and Alfredsson P H 1998 Eur. J. Mech. B 17 823

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