| Title:
|
Including eigenvalues of the plane Orr-Sommerfeld problem (English) |
| Author:
|
Klein, Peter P. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
6 |
| Year:
|
1993 |
| Pages:
|
452-458 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method. (English) |
| Keyword:
|
plane Orr-Sommerfeld problem |
| Keyword:
|
combination of Couette flow and Poiseuille flow |
| Keyword:
|
infinite dimensional matrix eigenvalue problem |
| Keyword:
|
inclusion of eigenvalues using a genralization of Gerschgorin's method |
| MSC:
|
34L40 |
| MSC:
|
47A75 |
| MSC:
|
65L15 |
| MSC:
|
76D99 |
| MSC:
|
76E05 |
| MSC:
|
76M25 |
| idZBL:
|
Zbl 0791.76025 |
| idMR:
|
MR1241448 |
| DOI:
|
10.21136/AM.1993.104567 |
| . |
| Date available:
|
2008-05-20T18:46:30Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104567 |
| . |
| Reference:
|
[1] Di Prima R. C., Habetler G. J.: A completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability.Arch. Rat. Mech. Anal. 34 (1969), 218-227. MR 0266499, 10.1007/BF00281139 |
| Reference:
|
[2] Donnelly J. D. P.: Bounds for the eigenvalues of non-self-adjoint differential operators.J. Inst. Math. Appl. 13 (1974), 249-261. Zbl 0287.65049, MR 0341883, 10.1093/imamat/13.2.249 |
| Reference:
|
[3] Lin C. C.: The theory of hydrodynamic stability.Cambridge University Press, 1955. Zbl 0068.39202, MR 0077331 |
| Reference:
|
[4] Klein P. P.: Zur Eigenwerteinschließung bei nichtselbstadjungierten Eigenwertaufgaben mit Differentialgleichungen.In ISNM 83, Numerische Behandlung von Eigenwertaufgaben, Band 4. Tagung in Oberwolfach 30.11.-6.12.86. Basel (Albrecht, J. u.a., eds.), Birkhäuser Verlag, 1987, pp. 130-144. Zbl 0627.65064, MR 1023878 |
| Reference:
|
[5] Klein P. P.: Eigenwerteinschließung bei nichtselbstadjungierten Eigenwertaufgaben.Z. angew. Math. Mech. 70 (1990), T560-T562. Zbl 0716.65078, MR 1070144 |
| Reference:
|
[6] Potter M. C.: Stability of plane Couette-Poiseuille flow.J. Fluid Mech. 24 (1966), 609-619. 10.1017/S0022112066000855 |
| Reference:
|
[7] Reynolds W. C., Potter M. C.: Finite-amplitude instability of parallel shear flows.J. Fluid Mech. 27 (1967), 465-492. Zbl 0166.46102, 10.1017/S0022112067000485 |
| . |
