1983
DOI: 10.1017/s0022112083001858
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On the stability of plane Poiseuille flow to finite-amplitude disturbances, considering the higher-order Landau coefficients

Abstract: In this work a study has been made of the Stuart (1960)–Watson (1960) formalism as applied to plane Poiseuille flow. In particular, the higher-order Landau coefficients have been calculated for the Reynolds & Potter (1967) method and for the Watson (1960) method. The results have been used to study the convergence of the Stuart–Landau series. A convergence curve in the (α, R)-plane has been obtained by using suitable Domb–Sykes plots. In the region of poor convergence of the series, and also in a part of t… Show more

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Cited by 38 publications
(51 citation statements)
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“…Later Crouch and Herbert (1993) . The same problem was also considered by Sen and Venkateswarlu (1983) and Fujimura (1989Fujimura ( , 1991Fujimura ( , 1997) whose papers will be discussed below. Zhou (1982) developed an improved version of the classical Stuart-Watson method of 1960, assuming that both the amplitude A(t) and the angular frequency ω 1 (t) of the unstable wave disturbance vary with time.…”
Section: Evaluation Of Coefficients Of Amplitude Equations and Equilimentioning
confidence: 95%
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“…Later Crouch and Herbert (1993) . The same problem was also considered by Sen and Venkateswarlu (1983) and Fujimura (1989Fujimura ( , 1991Fujimura ( , 1997) whose papers will be discussed below. Zhou (1982) developed an improved version of the classical Stuart-Watson method of 1960, assuming that both the amplitude A(t) and the angular frequency ω 1 (t) of the unstable wave disturbance vary with time.…”
Section: Evaluation Of Coefficients Of Amplitude Equations and Equilimentioning
confidence: 95%
“…Early comparisons of the available theoretical estimates with the experimental data by Nishioka et al (1975), referring to development of waves generated by a vibrating ribbon in a laboratory channel flow, seemed to support both the results by Itoh (1974a) and the conclusions of Herbert (1977). However, subsequent more careful analysis detected some appreciable discrepancies between theory and experimental data, apparently connected with three-dimensional effects affecting measurements by Nishioka et al and with some inaccuracies of Itoh's calculations; see, e.g., Zhou (1982); Herbert (1980Herbert ( , 1983a, and Sen and Venkateswarlu (1983). Another method for calculation of Landau's constant was proposed by Itoh (1977a); as was indicated by Davey (1978) and Herbert (1983b), this method differs from that of Reynolds and Potter (1967) only by rearrangement of the terms in some alive, to publish the revised edition of the book as a book by Andronov et al (1959) with a strange remark in the Preface (which was repeated in the English translation of 1966 too) that 'the name of one of the authors was by an unfortunate mistake not noticed on the title page of the first edition'.…”
Section: Evaluation Of Coefficients Of Amplitude Equations and Equilimentioning
confidence: 96%
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