Scaling of entrapped gas pocket slamming events at dissimilar Euler number

This work concerns the scaling of the pressure rise time inside a gas pocket that is trapped between a gravity wave and a rigid structure during a slamming event. The model experiments are assumed to have the same Froude number and reference pressure as the prototype. In this case, the pressure time history does not follow Froude scaling. However, in the case where the gas pocket is compressed and begins to oscillate, similar to the free oscillations of an under-damped mass-spring system, the pressure amplitude in full scale can be estimated using the procedure suggested by Lundgren. This type of phenomenon is observed when a breaking wave traps an air pocket at a vertical wall or when a wave traps an air pocket at the upper corner of a tank during sloshing at high filling. A drawback of Lundgren's procedure is that only the pressure amplitude can be scaled. Hence, the rise time of the pressure, which is important from a structural dynamics point of view, is not available. In this work, the pressure amplitude and rise time scaling procedure (PARTS) is derived, which provides the rise time of the pressure inside the gas pocket. The mathematical problem of the oscillating gas pocket is posed as a nonlinear ordinary differential equation, including initial conditions. This mathematical problem is fitted to the pressure amplitude and rise time obtained from model experiments. Then, the mathematical problem is scaled to the prototype scale and solved again to obtain the pressure amplitude and rise time at the prototype scale. The scaling procedure is compared with the results obtained using a nonlinear boundary element method. The results show that both the pressure amplitude and the rise time are scaled accurately for the investigated gas pocket slamming event.