Air–water dynamics and wave forcing mechanisms in a pneumatic long-wave tsunami generator

The pneumatic tsunami generator enables the generation of Froude-scaled long waves in laboratory flumes through controlled air-pressure variation within a sealed tank. The internal water height responds to pressure evolution above the free surface, which in turn initiates wave formation at the connected flume interface. This configuration represents a canonical pressure-driven free-surface problem in which compressible gas dynamics are coupled to an incompressible liquid through a moving interface within a sealed volume. A reduced-order model for the air–water dynamics is developed in two asymptotic regimes: a quasi-static hydrostatic formulation with incompressible air and a dynamic non-hydrostatic formulation that accounts for air compressibility and water-column inertia. The model incorporates mass conservation, pressure–volume relations, and valve-pump inflow and outflow dynamics to describe the nonlinear response of the tank and the resulting near-field wave signal. Experimental data from a pneumatic tsunami generator system are used to examine the water-height evolution and associated near-field response. Model predictions show strong agreement with experimental observations, validating the underlying physical mechanisms. The model captures key dynamical features, including amplitude modulation, phase lag between air pressure and free-surface motion, and the approach to equilibrium between pump extraction and valve inflow. More broadly, the results clarify the dynamical role of air compressibility in pressure-driven free-surface systems and provide insight into transient compressible–incompressible coupling in sealed fluid configurations. These findings establish a mechanistic foundation for understanding crest- and trough-led long-wave formation and for future integration with full wave-propagation models.