Simple asymptotics for the temporal spectrum of an Orr-Sommerfeld problem
We analyse asymptotic approximations to the eigenvalue relation for the even modes of plane Poiseuille flow for large but finite values of the Reynolds number. By using outer approximations which are valid in the complete sense, we obtain a result which is remarkably simple and for which the relativ...
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| Published in | Applied mathematics letters Vol. 13; no. 3; pp. 51 - 55 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.04.2000
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| Subjects | |
| Online Access | Get full text |
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| Abstract | We analyse asymptotic approximations to the eigenvalue relation for the even modes of plane Poiseuille flow for large but finite values of the Reynolds number. By using outer approximations which are valid in the complete sense, we obtain a result which is remarkably simple and for which the relative error is of order R−12. |
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| AbstractList | We analyse asymptotic approximations to the eigenvalue relation for the even modes of plane Poiseuille flow for large but finite values of the Reynolds number. By using outer approximations which are valid in the complete sense, we obtain a result which is remarkably simple and for which the relative error is of order R−12. |
| Author | Ng, B.S. Reid, W.H. |
| Author_xml | – sequence: 1 givenname: B.S. surname: Ng fullname: Ng, B.S. email: bng@math.iupui.edu – sequence: 2 givenname: W.H. surname: Reid fullname: Reid, W.H. |
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| Cites_doi | 10.1103/PhysRev.74.191 10.1017/S0022112071002842 10.1017/S002211207600147X |
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| Copyright | 2000 |
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| EndPage | 55 |
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| Keywords | Hydrodynamic stability Asymptotic analysis Eigenvalue relation Spectrum |
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| References | Mack (BIB2) 1976; 73 Drazin, Reid (BIB3) 1981 Orszag (BIB1) 1971; 50 Pekeris (BIB4) 1948; 74 Mack (10.1016/S0893-9659(99)00185-8_BIB2) 1976; 73 Drazin (10.1016/S0893-9659(99)00185-8_BIB3) 1981 Orszag (10.1016/S0893-9659(99)00185-8_BIB1) 1971; 50 Pekeris (10.1016/S0893-9659(99)00185-8_BIB4) 1948; 74 |
| References_xml | – volume: 73 start-page: 497 year: 1976 end-page: 520 ident: BIB2 article-title: A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer publication-title: J. Fluid Mech. contributor: fullname: Mack – volume: 50 start-page: 689 year: 1971 end-page: 703 ident: BIB1 article-title: Accurate solutions of the Orr-Sommerfeld stability equation publication-title: J. Fluid Mech. contributor: fullname: Orszag – year: 1981 ident: BIB3 article-title: Hydrodynamic Stability contributor: fullname: Reid – volume: 74 start-page: 191 year: 1948 end-page: 199 ident: BIB4 article-title: Stability of the laminar parabolic flow of a viscous fluid between parallel fixed walls publication-title: Phys. Rev. contributor: fullname: Pekeris – year: 1981 ident: 10.1016/S0893-9659(99)00185-8_BIB3 contributor: fullname: Drazin – volume: 74 start-page: 191 issue: 2 year: 1948 ident: 10.1016/S0893-9659(99)00185-8_BIB4 article-title: Stability of the laminar parabolic flow of a viscous fluid between parallel fixed walls publication-title: Phys. Rev. doi: 10.1103/PhysRev.74.191 contributor: fullname: Pekeris – volume: 50 start-page: 689 year: 1971 ident: 10.1016/S0893-9659(99)00185-8_BIB1 article-title: Accurate solutions of the Orr-Sommerfeld stability equation publication-title: J. Fluid Mech. doi: 10.1017/S0022112071002842 contributor: fullname: Orszag – volume: 73 start-page: 497 year: 1976 ident: 10.1016/S0893-9659(99)00185-8_BIB2 article-title: A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer publication-title: J. Fluid Mech. doi: 10.1017/S002211207600147X contributor: fullname: Mack |
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| Snippet | We analyse asymptotic approximations to the eigenvalue relation for the even modes of plane Poiseuille flow for large but finite values of the Reynolds number.... |
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| SubjectTerms | Asymptotic analysis Eigenvalue relation Hydrodynamic stability Spectrum |
| Title | Simple asymptotics for the temporal spectrum of an Orr-Sommerfeld problem |
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