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Generalized eigenfunction method for floating bodies

Published online by Cambridge University Press:  14 January 2011

COLM J. FITZGERALD  and
MICHAEL H. MEYLAN
COLM J. FITZGERALD
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
MICHAEL H. MEYLAN*
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
*
†Email address for correspondence: meylan@math.auckland.ac.nz
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Abstract

We consider the time domain problem of a floating body in two dimensions, constrained to move in heave and pitch only, subject to the linear equations of water waves. We show that using the acceleration potential, we can write the equations of motion as an abstract wave equation. From this we derive a generalized eigenfunction solution in which the time domain problem is solved using the frequency-domain solutions. We present numerical results for two simple cases and compare our results with an alternative time domain method.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 544 - 554
Copyright
Copyright © Cambridge University Press 2011

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References

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Fitzgerald and Meylan supplementary material

Movie 1. The solution for a circular body half immersed for the times shown. At t = 0 the heave ammplitude is 0.5 and all other displacements and velocities are zero.

Download Fitzgerald and Meylan supplementary material(Video)
Video 626.7 KB

Fitzgerald and Meylan supplementary material

Movie 2. The solution for a dock of negligible submergence for the times shown. At t = 0 the heave amplitude is 0.5 and the pitch amplitude is π / 16 and all other displacements and velocities are zero.

Download Fitzgerald and Meylan supplementary material(Video)
Video 802.8 KB

Fitzgerald and Meylan supplementary material

Movie 3. The solution for a circular body half immersed for the times shown. At t = 0 the heave amplitude is 0.5, the surface displacement is exp(-4(x+3)2) and all velocities are zero.

Download Fitzgerald and Meylan supplementary material(Video)
Video 882.7 KB

Fitzgerald and Meylan supplementary material

Movie 4. The solution for a dock of negligible submergence for the times shown. At t = 0 the heave amplitude is 0.5 and the pitch amplitude is π / 16, the surface displacement is exp(-4(x+3)2) and all velocities are zero.

Download Fitzgerald and Meylan supplementary material(Video)
Video 1 MB