Depth-integrated equation for large-scale modelling of low-frequency hydroacoustic waves

Sammarco, Paolo; Cecioni, Claudia; Bellotti, Giorgio; Abdolali, Ali

doi:10.1017/jfm.2013.153

Cited by 39 publications

(55 citation statements)

References 13 publications

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“…The paper aims to: (i) review Sammarco et al (2013)'s formulation of the mild-slope equation for compressible fluids to derive a form that is solvable analytically in a 3D domain (see §2), (ii) obtain a new analytical solution of the model equation (see §3) and (iii) identify the physical nature of the different kinds of HA frequencies excited by tsunamigenic disturbances over a non-uniform bottom in 3D (see §4).…”

Section: E Renzimentioning

confidence: 99%

“…Calling on Sammarco et al (2013), consider the motion of a slightly compressible fluid of density ρ = ρ 0 + ρ , where ρ 0 is the constant ambient density and ρ ρ 0 is a small perturbation due to compressibility. Let (x, z) = (x, y, z) describe the coordinate of a point in a three-dimensional fluid domain D, with the z axis orthogonal to the horizontal (x, y) plane and pointing upwards from the unperturbed water level z = 0.…”

Section: Model Equationsmentioning

confidence: 99%

“…Also, ∇f (x) = (f x , f y ) is the 2D gradient and subscripts denote differentiation with respect to the relevant variable. The system (2.1)-(2.3) describes acoustic-gravity waves generated by the bottom disturbance H and is the same as that considered by Sammarco et al (2013). In this paper we shall develop a mathematical method to solve the system of governing equations (2.1)-(2.3) analytically.…”

Section: Model Equationsmentioning

confidence: 99%

“…Re {·} denotes the real part and will be omitted in the following for the sake of brevity. Results for generic time-dependent disturbances can be found by Fourier superposition of the harmonic solution Φ (Mei et al 2005;Sammarco et al 2013). Using (2.4), the system (2.1)-(2.3) becomes…”

Section: Model Equationsmentioning

confidence: 99%

“…However, and Kadri (2015)'s results cannot be applied to a 3D geometry, where the combined effect of shoaling and refraction dramatically alters the propagation dynamics with respect to the 2D scenario. A significant advancement in the field is represented by the seminal work of Sammarco et al (2013), who for the first time derived a 3D form of the mild-slope equation for weakly compressible fluids (MSEWC) and solved it numerically. Sammarco et al (2013)'s numerical solution of the model equation, however, does not discriminate explicitly between the eigenfrequencies of the HA modes and how they transform as they propagate.…”

Section: Introductionmentioning

confidence: 99%

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

Renzi

2016

J. Fluid Mech.

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This draft was prepared using the LaTeX style file belonging to the Journal We present a novel analytical solution for hydro-acoustic waves in a weakly compressible fluid over a slowly varying bottom. Application of a multiple-scale perturbation technique and matched asymptotic analysis leads to a uniform analytical solution of the depthaveraged governing equations in three dimensions. We show that the slow depth variation plays a leading-order effect on the evolution of the normal mode amplitude and direction. This dynamics is much richer than the two-dimensional limit analysed in previous studies.For tsunamigenic disturbances, we show that the hydro-acoustic wave field is made up by longshore trapped and offshore propagating components, which were not explicated in previous work. For a plane beach, we find an exact analytical solution of the model equation in terms of integrals of Bessel functions. Our model offers a physical insight into the evolution of hydro-acoustic waves of interest for the design of tsunami early warning systems.

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Section: E Renzimentioning

confidence: 99%

Section: Model Equationsmentioning

confidence: 99%

Section: Model Equationsmentioning

confidence: 99%

Section: Model Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Renzi

2016

J. Fluid Mech.

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Hydro‐acoustic and tsunami waves generated by the 2012 Haida Gwaii earthquake: Modeling and in situ measurements

et al. 2015

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Detection of low-frequency hydro-acoustic waves as precursor components of destructive tsunamis can enhance the promptness and the accuracy of Tsunami Early Warning Systems (TEWS). We reconstruct the hydro-acoustic wave field generated by the 2012 Haida Gwaii tsunamigenic earthquake using a 2-D horizontal numerical model based on the integration over the depth of the compressible fluid wave equation and considering a mild sloped rigid seabed. Spectral analysis of the wave field obtained at different water depths and distances from the source revealed the frequency range of low-frequency elastic oscillations of sea water. The resulting 2-D numerical model gave us the opportunity to study the hydro-acoustic wave propagation in a large-scale domain with available computers and to support the idea of deep-sea observatory and data interpretation. The model provides satisfactory results, compared with in situ measurements, in the reproduction of the long-gravitational waves. Differences between numerical results and field data are probably due to the lack of exact knowledge of sea bottom motion and to the rigid seabed approximation, indicating the need for further study of poro-elastic bottom effects.

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Pressure field induced in the water column by acoustic‐gravity waves generated from sea bottom motion

Oliveira

Kadri

2016

JGR Oceans

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An uplift of the ocean bottom caused by a submarine earthquake can trigger acoustic‐gravity waves that travel at near the speed of sound in water and thus may act as early tsunami precursors. We study the spatiotemporal evolution of the pressure field induced by acoustic‐gravity modes during submarine earthquakes, analytically. We show that these modes may all induce comparable temporal variations in pressure at different water depths in regions far from the epicenter, though the pressure field depends on the presence of a leading acoustic‐gravity wave mode. Practically, this can assist in the implementation of an early tsunami detection system by identifying the pressure and frequency ranges of measurement equipment and appropriate installation locations.

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Depth-integrated equation for large-scale modelling of low-frequency hydroacoustic waves

Cited by 39 publications

References 13 publications

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

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

Hydro‐acoustic and tsunami waves generated by the 2012 Haida Gwaii earthquake: Modeling and in situ measurements

Pressure field induced in the water column by acoustic‐gravity waves generated from sea bottom motion

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