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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 181
Wave-Current Interaction with a Vertical Cylinder in Cross Flow: A Semi-Analytical Approach I.K. Chatjigeorgiou, S.A. Mavrakos and N.I. Xiros
School of Naval Architecture and Marine Engineering, National Technical University of Athens, Greece Full Bibliographic Reference for this paper
I.K. Chatjigeorgiou, S.A. Mavrakos, N.I. Xiros, "Wave-Current Interaction with a Vertical Cylinder in Cross Flow: A Semi-Analytical Approach", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 181, 2006. doi:10.4203/ccp.84.181
Keywords: potential theory, waves, current, inhomogeneous condition, semi-analytical formulation, Sturm-Liouville problem.
Summary
The scope of the present paper is the derivation of a semi-analytical formulation
for the first-order diffraction potential due to the presence of a vertical
surface-piercing cylinder in a flow field in which waves and currents coexist. The specific
subject is very important for offshore applications in which floating or fixed
structures usually consist of cylindrical elements. In addition the wave-current
interaction with a floating structure may be regarded as the opposite problem of the
structure moving with a slow speed in a wave field. Usually the methods
implemented for treating this problem are numerical [1,2]. This is due to the fact
that the presence of the current is accommodated in the free surface boundary
condition which in turn becomes inhomogeneous. The inhomogeneous form of the
associated equation makes the analytical approach of the solution more difficult for
the diffraction potential. On the other hand the derivation of a closed-form solution
for the scattered velocity potential due to the presence of a structure within the
wave-current flow field provides a robust and reliable tool for calculating the
induced hydrodynamic forces, the wave drift damping and the wave run-up on the
structural elements. In the present work this is performed by seeking a
semi-analytical formulation for the diffraction potential of the resulting complex flow
field.
As mentioned before, the main difficulty arises from the boundary condition on the free surface for which it can be shown that it is given by the following relation.
where ![]() ![]() ![]() ![]() ![]() ![]() ![]()
where ![]() ![]() ![]()
The results presented in the paper depict the variation of the complex effective
pressure distribution for various eigenmodes. It is shown that although this term is
convergent for
References
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