Nonlinear viscous waves produced by an impulsively moving plate
Abstract
The freesurface flow generated by an impulsively accelerating, surfacepiercing, vertical plate was studied numerically as well as experimentally. The twodimensional, unsteady NavierStokes equations are discretized using the finiteanalytic scheme which incorporates the analytic solution into the locally linearized differential equations. The continuity equation and the dynamic boundary conditions on normal and tangential stresses at the free surface are applied to determine the pressure and two velocity components at the free surface. The kinematic boundary condition on the free surface provides the movement of the free surface. A series of experiments is carried out in an open channel with a constant water depth. The flat vertical plate is fixed on a towing carriage which is set off by suddenly dropping a weight bucket through a connecting steel cable in a pulley system. The freesurface profile ahead of the plate and the pressure distribution on the plate surface are measured. The flow field around the moving contact line is studied by applying the present numerical code. The contact angle between the free surface and the vertical plate is found to be very close to that formed by the free surface of a fluid contained in a rectangular tank which moves with the same constant acceleration. The velocity of the moving contact line is thereby derived as a function of the acceleration of the plate based on the principle of the conservation of mass. The propagation of waves produced by a moving plate along the channel is also investigated numerically. The propagation speed of generated waves is close to that of shallowwater waves with small amplitudes. An empirical formula for the ultimate maximum wave amplitude is obtained as a function of the displacement and the acceleration of the plate.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.........9Y
 Keywords:

 Flow Distribution;
 NavierStokes Equation;
 Nonlinear Systems;
 Pressure Distribution;
 Stress Analysis;
 Unsteady Flow;
 Viscosity;
 Water Waves;
 Boundary Conditions;
 Continuity Equation;
 Flat Plates;
 Vertical Orientation;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer