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Titolo: Asymptotic analysis of a fourthorder turningpoint problem in hydrodynamic stability
Autore: Ng, BS; Reid, WH;
 Indirizzi:
 Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA Indiana Univ Purdue Univ Indianapolis IN USA 46202 anapolis, IN 46202 USA
 Titolo Testata:
 QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS
,
volume: 53,
anno: 2000,
parte:, 1
pagine: 27  42
 SICI:
 00335614(200002)53:<27:AAOAFT>2.0.ZU;2A
 Fonte:
 ISI
 Lingua:
 ENG
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Engineering, Computing & Technology
 Citazioni:
 10
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Ng, BS Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USAIndiana Univ Purdue Univ Indianapolis IN USA 46202 s, IN 46202 USA



 Citazione:
 B.S. Ng e W.H. Reid, "Asymptotic analysis of a fourthorder turningpoint problem in hydrodynamic stability", Q J MECH AP, 53, 2000, pp. 2742
Abstract
An asymptotic analysis is made of the socalled Pekeris modes of the OrrSommerfeld problem for plane Poiseuille flow. These are damped modes of the 'centre' or 'fast' type for which c(r) up arrow 1 and c(i) up arrow 0 as alpha R > infinity. The numerical results obtained by Orszag (J. Fluid Mech. 50 (1971) 689) for alpha = 1 and R = 10 000 showed that the eigenvalues for the even and odd modes of this type are very nearly equal, and one of the goals of this paper is to provide an analytical explanation for this rather striking result. Under certain simplifying assumptions we are led to a fourthorder equation which can be viewed as a generalization of Weber's equation for the parabolic cylinder functions. The eigenvalue problem is then posed on an infinite interval and we find that the eigenvalue relations forthe even and odd modes are indeed the same even though the underlying analysis is significantly different in the two cases. Explicit results are alsogiven for both the even and odd eigenfunctions; The even eigenfunctions are similar to the Whittaker functions Dn(x) but the odd eigenfunctions involve Dawson's integral and certain polynomials.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 22/09/20 alle ore 16:29:42