Space–time statistics of 2D soliton gas in shallow water studied by stereoscopic surface mapping

We describe laboratory experiments in a 2D wave tank that aim at building up and monitor 2D shallow water soliton gas. The water surface elevation is obtained over a large ( \(\sim 100\,\text {m}^2\) $\sim 100{\text{m}}^2$ ) domain, with centimeter-resolution, by stereoscopic vision using two cameras. Floating particles are seeded to get surface texture and determine the wave field by image correlation. With this setup, soliton propagation and multiple interactions can be measured with a previously unreachable level of detail. The propagation of an oblique soliton is analyzed, and the amplitude decay and local incidence are compared to analytical predictions. We further present two cases of 2D soliton gas, emerging from multiple line solitons with random incidence ( \(|\theta |<30^\circ\) $|\theta |<{30}^{\circ }$ ) and from irregular random waves forced with a JONSWAP spectrum ( \(|\theta |<45^\circ\) $|\theta |<{45}^{\circ }$ ). To our knowledge, those are the first observations of random 2D soliton gas for gravity waves. In both cases, Mach reflections and Mach expansions result in solitons that mainly propagate in directions perpendicular to the wavemakers.