The sliding force was a contributing factor to the displacement of caissons from the Kamaishi composite breakwater during the Great East Japan tsunami 2011 (Arikawa et al., 2012). The pressure reduction on the landward wall of the caisson due to non-aeration of the overflowing jet gives rise to an additional horizontal force which increases the sliding force. The estimation of this additional horizontal force and the proper understanding of the physical processes which cause it are imperative in establishing stability of a caisson breakwater during tsunami overtopping.
Tsunami is associated with accelerating flows with massive heads that results in detached overflow nappes. In this research, a simplified tsunami was modelled in the laboratory as a steady breakwater overflow and the respective pressure drop behind the overflow nappe is derived. The nappe trajectories are derived theoretically based on general projectile motion for both the aerated and non-aerated scenarios. This ballistic model is validated using measurements of the physical model. For the aerated nappe, the theoretical results and measurements are in agreement. For the non-aerated nappe, the ballistic model provides comparatively high deviations from the measured nappe. A sensitivity analysis of pressure reduction indicates the deviations can be attributed to the derived pressure drops.
In addition, the governing physical processes related to caisson breakwater overflowing are investigated. The flow conditions below the overflow nappe are hydrostatic, which is implied by a time-averaged stationary water level below the nappe. The dynamic pressure arising from the stagnation pressure at the jet impingement on the flume bed is estimated and is compared with the pressure drop behind the nappe. The results suggest the above-mentioned dynamic pressure is negligible with respect to the pressure drop. Thus, it is concluded that the governing mechanism responsible for the pressure reduction is the air entrainment process during jet impingement. The air entrainment rate from the cavity behind the nappe is compared against the impinging velocity of the overflow jet. The results suggest that air entrainment rate increases with increasing jet impingement velocity, establishing the fact that higher inertia forces leads to rapid air entrainment.
The ratio of additional horizontal force due to non-aeration to the total horizontal force is found to be between 0.15 and 0.25. However, some eccentricities are evident with extreme tail water depths and flow rates. Scaled-up forces are obtained using Froude scaling criteria. Reynolds numbers suggest that the flow is fully turbulent at both the lab and field scales, while Weber numbers show that surface tension effects might be more pronounced in the lab than in the field.
As surface tension effects may affect the direct scaling up of model tests to field scale, the utility of numerical model simulations is apparent. In OpenFOAM, the k-epsilon turbulence model with the InterFoam solver is used for this purpose. Prior to investigating the validity of OpenFOAM to simulate the caisson overflowing scenario, the model is validated for open channel flow. The results indicate that OpenFOAM correctly simulates the open channel flow with respect to the logarithmic profile and the free-surface slope. Furthermore, simulation of the flow atop the caisson very closely matches that of the physical laboratory model test. The model results for nappe behaviour follows existing trends found in literature. The simulated overflow nappe is a clinging nappe rather than a detached one due to the inability of the 2D model to allow air into the void behind the nappe.
The significance of the present study has various aspects. The ballistic model enables the derivation of the nappe’s trajectories during steady overflow of a caisson breakwater. As a result, an explicit relationship between kinematics (ballistics) and dynamics (forces) can be developed. The estimation of the additional horizontal force due to non-aeration effects pave the way to improve design guidelines for the stability of caisson breakwaters during tsunami overtopping.