Hydro-acoustic precursors of gravity waves generated by surface pressure disturbances localised in space and time

Abstract

Citation: RENZI, E. and DIAS, F., 2014. Hydro-acoustic precursors of gravity waves generated by surface pressure disturbances localised in space and time. We consider the mechanics of coupled underwater-acoustic and surface-gravity waves generated by surface pressure disturbances in a slightly compressible fluid. We show that pressure changes on the ocean surface, localised in space and time, can induce appreciable underwater compression waves which are precursors of the surface gravity waves. Although the physical properties of acoustic-gravity waves have already been discussed in the literature, such dynamics was not investigated in previous studies. We derive new results for the underwater compression wave field and discuss the dynamics of its generation and propagation. This work could lead to the design of innovative alert systems for coastal flooding management.

Hydro-acoustic frequencies of the weakly compressible mild-slope equation

“…As anticipated in §2.1, a good approximation for the HA wavenumbers β n = iβ n is 16) see for example Yamamoto (1982), Stiassnie (2010) and Renzi & Dias (2014a). As a consequence, the eigenmodes (2.9) become…”

“…The 0th mode represents the surface gravity wave, which is hardly influenced by compressibility (Yamamoto 1982;Stiassnie 2010;Renzi & Dias 2014a). The higher modes n > 0 represent the associated HA waves, which for given frequency ω can be either evanescent or propagating at large |x|, depending on the system parameters (see §3).…”

“…This happens precisely because the HA frequencies turn away as they approach the shore (see again §3). The dynamic pressure can be determined from the HA potential with the expression p n (x, z, t) = −ρ 0 Φ nt (see Renzi & Dias 2014a), which yields p n (x, z, t) = p t n (x, z, t) + p p n (x, z, t). In the latter,…”

“…Stiassnie (2010) was among the first to derive an analytical model of gravity and HA wave generation by a tsunamigenic bottom deformation in uniform water depth. Later, Renzi & Dias (2014a) solved a similar problem, but with the forcing term being a localised surface pressure perturbation in space and time. The propagation of HA waves generated by bottom movements over a range dependent environment is a more complex problem.…”

Large-scale numerical modeling of hydro-acoustic waves generated by tsunamigenic earthquakes

“…The potential tsunamis can therefore be destructive since the coasts are densely populated and very close: the travel time of tsunami wave towards the coast is in the order of few minutes up to 1 h. Rapid detection of the tsunami generation in this region is mandatory for future development of early warning systems, and the use of the hydro-acoustic signals can cope with this necessity. This appealing feature of hydro-acoustic waves has recently been considered by Renzi and Dias (2014) for the wave field generated by a localized surface pressure disturbance; their work could lead to the design of innovative alert systems for coastal flooding management, based on the measurements of hydro-acoustic wave.…”