We study the non-linear decay motion of a 2D plate experimentally and analytically. The plate was hinged to the bottom of a wave flume and was positioned at a certain initial angle. The restoring force on the plate was derived from two horizontal pre-tensioned springs. To maintain the system characteristics linear, the springs were selected to allow a maximum 18 degrees of rotation for the plate. The position, velocity and the acceleration of the plate were retrieved from the load cells attached to the springs. The plate was released from its initial position at t = 0 and allowed to oscillate. The free-surface elevation was captured using a high frame per second (200 fps) digital camera. In addition, two wave probes on either side of the plate were installed. It was observed that the high stiffness of the springs produced a mild impact to the water that caused a relatively large water run-up and water jet. This event, consequently, made the decay motion very non-linear. A formulation based on the linear theory was developed to help with the understanding and interpreting the physics of the problem. The presented experiment aims to benchmark various numerical techniques such as Smoothed Particle Hydrodynamics (SPH) that intend to simulate free-surface and water impact problems. Although the setup did not model a green water incident, most of the features in the problem, like initial water impact, run up and water jet resemble the physics of green water. In the designed experiment, not only body 3D effects were minimum, but also the system characteristics were linear. Moreover, in contrast to the dam break experiments, perfect initial conditions were achieved. Therefore, the effects of the flow nonlinearities such as the plate impact to the water, water run up-down and water jet were studied without interference of the body nonlinearities. The impact of these effects on the damping and the added mass were highlighted.
Quadratic autocatalysis with non-linear decay. II: the effect of incomplete mixing