Initial stage of plate lifting from a water surface

• Published in: Journal of engineering mathematics Vol. 102; no. 1; pp. 117 - 130
• Main Authors: Korobkin, Alexander, Khabakhpasheva, Tatyana, Rodríguez-Rodríguez, Javier
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-02-2017; Springer Nature B.V
• Subjects: Acceleration; Applications of Mathematics; Boundary element method; Computational Mathematics and Numerical Analysis; Constants; Flat plates; Flow velocity; Free surfaces; Hoisting; Hydrodynamic pressure; Mathematical analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinearity; Potential flow; Self-similarity; Suction; Surface tension; Theoretical and Applied Mechanics; Time dependence; Two dimensional flow; 76B10; Water exit; Matched asymptotics; Free-surface flows; Numerical methods
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-015-9832-8

This study deals with the flow induced by a rigid flat plate of finite length, initially touching a horizontal water surface, when it starts to move upwards with constant acceleration. In the present model, negative hydrodynamic pressures on the lower (wetted) surface of the plate are allowed, and thus, the water follows the plate due to the resulting suction force. The acceleration of the plate and the plate length are such that gravity, surface tension and viscous effects can be neglected during the early stages of the motion. Under these assumptions, the initial two-dimensional, potential flow caused by the plate lifting is obtained by using the small-time expansion of the velocity potential. This small-time solution is not valid close to the plate edges, as it predicts there singular flow velocities and unbounded displacements of the water-free surface. It is shown that close to the plate edges the flow is nonlinear and self-similar to leading order. This nonlinear flow is computed by the boundary-element method combined with a time-marching scheme. The numerical time-dependent solution approaches the self-similar local solution with time.