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Titolo:
Asymptotic analysis of a fourth-order turning-point 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:
0033-5614(200002)53:<27:AAOAFT>2.0.ZU;2-A
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 fourth-order turning-point problem in hydrodynamic stability", Q J MECH AP, 53, 2000, pp. 27-42

Abstract

An asymptotic analysis is made of the so-called Pekeris modes of the Orr-Sommerfeld 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 fourth-order 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 D-n(x) but the odd eigenfunctions involve Dawson's integral and certain polynomials.

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Documento generato il 22/09/20 alle ore 16:29:42