Including eigenvalues of the plane Orr-Sommerfeld problem
Applications of Mathematics (1993)
- Volume: 38, Issue: 6, page 452-458
- ISSN: 0862-7940
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topKlein, Peter P.. "Including eigenvalues of the plane Orr-Sommerfeld problem." Applications of Mathematics 38.6 (1993): 452-458. <http://eudml.org/doc/15765>.
@article{Klein1993,
abstract = {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.},
author = {Klein, Peter P.},
journal = {Applications of Mathematics},
keywords = {plane Orr-Sommerfeld problem; combination of Couette flow and Poiseuille flow; infinite dimensional matrix eigenvalue problem; inclusion of eigenvalues using a genralization of Gerschgorin's method; infinite-dimensional matrix eigenvalue problem; Gerschgorin's method; Poiseuille flow; Couette flow},
language = {eng},
number = {6},
pages = {452-458},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Including eigenvalues of the plane Orr-Sommerfeld problem},
url = {http://eudml.org/doc/15765},
volume = {38},
year = {1993},
}
TY - JOUR
AU - Klein, Peter P.
TI - Including eigenvalues of the plane Orr-Sommerfeld problem
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 6
SP - 452
EP - 458
AB - 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.
LA - eng
KW - plane Orr-Sommerfeld problem; combination of Couette flow and Poiseuille flow; infinite dimensional matrix eigenvalue problem; inclusion of eigenvalues using a genralization of Gerschgorin's method; infinite-dimensional matrix eigenvalue problem; Gerschgorin's method; Poiseuille flow; Couette flow
UR - http://eudml.org/doc/15765
ER -
References
top- Di Prima R. C., Habetler G. J., 10.1007/BF00281139, Arch. Rat. Mech. Anal. 34 (1969), 218-227. (1969) MR0266499DOI10.1007/BF00281139
- Donnelly J. D. P., 10.1093/imamat/13.2.249, J. Inst. Math. Appl. 13 (1974), 249-261. (1974) Zbl0287.65049MR0341883DOI10.1093/imamat/13.2.249
- Lin C. C., The theory of hydrodynamic stability, Cambridge University Press, 1955. (1955) Zbl0068.39202MR0077331
- 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. (1987) Zbl0627.65064MR1023878
- Klein P. P., Eigenwerteinschließung bei nichtselbstadjungierten Eigenwertaufgaben, Z. angew. Math. Mech. 70 (1990), T560-T562. (1990) Zbl0716.65078MR1070144
- Potter M. C., 10.1017/S0022112066000855, J. Fluid Mech. 24 (1966), 609-619. (1966) DOI10.1017/S0022112066000855
- Reynolds W. C., Potter M. C., 10.1017/S0022112067000485, J. Fluid Mech. 27 (1967), 465-492. (1967) Zbl0166.46102DOI10.1017/S0022112067000485
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