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  • 1
    Electronic Resource
    Electronic Resource
    Evolution of some isolated disturbances to Jeffery–Hamel flow (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 3838-3840 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of Jeffery–Hamel flow in a divergent wedge is considered by means of some initially localized disturbances, whose evolution downstream with time is studied by an integral of fixed frequency modes with respect to the frequency parameter. It is found, typically, that even in regions of parameter space that are nominally "unstable,'' the original localized disturbance grows very little before decaying downstream.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866423
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the solution for steady state and time dependent flows in certain channels with small wall curvature (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 169-189 
    Details
    ISSN: 0271-2091
    Keywords: Jeffery-Hamel ; Orr-Sommerfeld ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An asymptotic scheme is presented for the solution of the steady state and time dependent stream functions for flows in symmetric curved walled channels. In this scheme a class of non-linear Jeffery-Hamel solutions appear at O(1), and thus provide the first approximation to the steady state stream function. This class of Jeffery-Hamel solutions are evaluated by using a simple perturbation about Poiseuille flow.The classic Orr-Sommerfeld eigenproblem appears at O(1) in the asymptotic development of the time dependent stream function, but here there is a slow streamwise dependence. This eigenvalue problem, for a complex wave number, is solved using an algorithm which automatically provides an initial guess which is then used to iterate to the correct eigenvalue.Higher order terms in the asymptotic development, for both the steady state and time dependent stream functions, are evaluated to provide a solution for the total stream function.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050206
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  • 3
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    Evolution of some isolated disturbances to Jeffery–Hamel flow (1987)
    American Institute of Physics
    Details
    Publication Date: 1987-01-01
    Print ISSN: 0031-9171
    Topics: Physics
    Published by American Institute of Physics
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  • 4
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    The stability of flows in channels with small wall curvature (1985)
    Cambridge University Press
    Details
    Publication Date: 1985-10-01
    Description: The ‘stability’ of flows in symmetric curved-walled channels is investigated by essentially combining Fraenkel’s ‘small’ wall-curvature theory with the multiple-scaling (or WKB) method. The basic flow is characterized by the steady-state stream function Ω, which varies ‘ slowly ’ in the streamwise direction. An asymptotic scheme is posed for Ω in such a way that at lowest order Ω represents a class of Jeffery-Hamel solutions. An infinitesimal disturbance is superimposed on the basic flow through a time-dependent stream function Φ, and the resulting linearized disturbance equation suggests that fixed-frequency disturbances with ‘slowly’ varying wavenumber are appropriate. The asymptotic scheme for Φ yields the Orr-Sommerfeld equation at lowest order. Two classes of channels are considered. In the first class the curvature is constant in sign, and under certain conditions they reduce to symmetric divergent straight-walled channels. In the second class of channels the curvature varies in sign, and these may be more suitable for experimentation. A spatially dependent growth rate of the disturbance relative to the basic flow is defined; this forms the basis of the ‘stability’ analysis. Critical Reynolds numbers are deduced, below which the disturbance decays as it travels downstream, and above which the disturbance grows for a limited range in the streamwise direction. For the first class of channels the ‘ stability ’ analysis is carried out locally, and the dependence of the critical Reynolds numbers on curvature and higher-order terms is investigated. For the second class of channels the ‘stability’ analysis is carried out at various positions downstream, and an overall minimum critical Reynolds number is predicted for a range of channels and flows. © 1985, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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