Linear stern waves in finite depth channels
Author(s)
McCue, Scott William
Stump, D. M.
Griffith University Author(s)
Year published
2000
Metadata
Show full item recordAbstract
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 ...
View more >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.
View less >
View more >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
Subject
Applied Mathematics
Civil Engineering
Mechanical Engineering