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  • Linear stern waves in finite depth channels

    Author(s)
    McCue, Scott William
    Stump, D. M.
    Griffith University Author(s)
    McCue, Scott W.
    Year published
    2000
    Metadata
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    Abstract
    This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised ...
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    This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.
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    Journal Title
    Quarterly Journal of Mechanics and Applied Mathematics
    Volume
    53
    Issue
    4
    DOI
    https://doi.org/10.1093/qjmam/53.4.629
    Subject
    Applied Mathematics
    Civil Engineering
    Mechanical Engineering
    Publication URI
    http://hdl.handle.net/10072/59213
    Collection
    • Journal articles

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