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The nonlinear problem of a gliding body with gravity

Published online by Cambridge University Press:  14 June 2013

Y. A. Semenov  and
G. X. Wu
Y. A. Semenov
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK Institute of Hydromechanics of the NAS of Ukraine, Kiev 03057, Ukraine
G. X. Wu*
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: g.wu@ucl.ac.uk
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Abstract

Analysis based on the velocity potential free flow theory with the fully nonlinear boundary condition is made for the steady flow generated by a body gliding along a free surface. Employing the integral hodograph method, we derive analytical expressions for the complex velocity and for the derivative of the complex potential with the coordinate of a parameter plane. The boundary value problem is transformed into a system of two integro-differential equations for the velocity modulus on the free surface and for the slope of the wetted body surface in the parameter plane. The same slope and curvature of the free surface and the body surface at the intersection are adopted to determine the separation points of the flow and from the body. Numerical results are provided for a gliding flat plate and a circular cylinder. The pressure distribution along the body and the free surface shape are presented for a wide range of Froude numbers, within the limit for which the solution corresponding to non-breaking waves downstream can be obtained.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 132 - 160
Copyright
©2013 Cambridge University Press 

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