TY - JOUR

T1 - Initial stage of plate lifting from a water surface

AU - Korobkin, Alexander

AU - Khabakhpasheva, Tatyana

AU - Rodríguez-Rodríguez, Javier

N1 - © The Author(s) 2015. This article is published with open access at Springerlink.com

PY - 2017/2

Y1 - 2017/2

N2 - 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.

AB - 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.

KW - Free-surface flows

KW - Matched asymptotics

KW - Numerical methods

KW - Water exit

UR - http://www.scopus.com/inward/record.url?scp=84951960606&partnerID=8YFLogxK

U2 - 10.1007/s10665-015-9832-8

DO - 10.1007/s10665-015-9832-8

M3 - Article

AN - SCOPUS:84951960606

VL - 102

SP - 117

EP - 130

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 1

ER -