· · · Repository Hydraulic Engineering Reports

Shock pressures of high intensity and short duration may occur during breaking of waves on coastal structures, slamming of ships, landing of seaplanes, and water entry of naval projectiles with flat nose. The phenomenon of shock pressures resulting from the impact between a solid and a liquid can better be described as a water hammer phenomenon wherein the elasticity of the solid and the compressibility of the liquid are the governing factors. The water hammer theory predicts the extreme values of shock pressures since it neglects the effect of air that might be entrapped between the solid an the liquid at the moment of impact. Analytical formulations of shock pressures as a water hammer phenomenon and as the compression of a thin layer of air entrapped between the solid and the liquid at the moment of impact are presented in this report. Tests were conducted by dropping a steel, aluminum or plastic plate whose edge was hinged at the water surface into a 3- by 3- by 6-ft steel tank that was partially filled with water. The shock pressures were measured at two locations by means of strain gage and piezoelectric type pressure cells mounted in the plate with special adapters. The ratio between the recorded and theoretical pressures when treated statistically was found to fit the Poisson distribution well. Correlation between the recorded pressures and the shape of the surface of contact between the solid and the liquid at the moment of impact indicated that although shock pressures have a great intensity, they have a short duration and occur only at some spots on the surface of the solid. Therefore (a) they should not be applied as static pressure for checking the stability of the coastal structure as a whole, (b) they may be absorbed by flexible structures, (c) they may cause cracks in rigid structures such as steel caissons filled with rock, and (d) they may affect the stability of structures that have natural frequencies within the range of duration of shock pressures. Equations and diagrams for the prediction of the magnitude and duration of shock pressures resulting from the impact between a solid and a liquid are presented herein.

Experimental research to the influence of the air pressure on the impact pressure cause by breaking waves. The research shows that there are three factors which load the structure during the breaking of waves: the water layer over the structure, the shock due to the impact of the water jet from breaking and the air pocket entrapped in the water mass. The influence of all of the factors is determined.

The characteristic motion of water under breaking waves and the turbulence structure in the surf zone were investigated through detailed two-dimensional velocity measurements in a wave flume. Significant difference was found between the breaking processes in the outer and inner regions of the surf zone. The velocity field in each region consists of steady current, periodic wave motion, organized vortex motion and turbulence. It was found that the organized vortex motion caused by wave breaking was an important fluid motion connecting the wave motion and the turbulence. The vertical profiles of the undertow, which is the steady current below the wave trough level, were investigated from velocity histories measured by hot-film and laser-Doppler-velocimeters. The turbulence generated in the upper layer by wave breaking prevents the development of the bottom boundary layer in the inner region. The vertical distribution of the mean Reynolds stress and the mean eddy viscosity coefficient in the inner region can be approximated by linear functions of the vertical elevation. The offshore-directed mean shear stress on the bottom is so large that it can not be neglected in the modeling of the undertow. The transition point which was the boundary between the outer and inner regions of the surf zone was defined as the offshore limit of the quasi-steady breaking region. The distance from the breaking point to the transition point was expressed in terms of the breaking water depth and the bottom slope. In order to describe the mechanism of the energy transfer during wave breaking accurately, a model was presented in which the organized large vortexes were taken into account as a transmitter of energy in the energy transfer process from wave motion to turbulence. The distribution of the turbulence energy calculated by this model agreed with the experimental results qualitatively. The mass and momentum fluxes by the organized large vortexes were also discussed. The mass transport by breaking waves was found to be induced by the wave motion and the organized large vortexes. By using the models of the energy distribution and the mass transport, a model was presented for the two-dimensional distribution of the undertow. The Reynolds stress and the eddy viscosity coefficient were quantitatively evaluated from the energy dissipation rate on the basis of the dimensional analysis. The variation of the mean water level in the surf zone was also predicted with a good accuracy by considering the momentum flux by the organized vortexes. The model can evaluate the distribution of the undertow on an arbitrary beach topography from the incident wave condition.