Role of Compressibility on Tsunami Propagation

Abdolali, Ali; Kirby, James T.

doi:10.1002/2017jc013054

Cited by 33 publications

(13 citation statements)

References 24 publications

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“…Actually, one can omit the gravity contribution in (2.1) for practical purposes. This conclusion was also confirmed by Abdolali & Kirby (2017), who showed the negligible role of g(∂ϕ/∂z) on hydroacoustic waves and surface gravity waves with short wavelength. Furthermore, we investigate different cases in a similar way, as shown in table 6.…”

Section: Resonant Wavessupporting

confidence: 67%

On the steady-state resonant acoustic–gravity waves

2018

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The steady-state interaction of acoustic–gravity waves in an ocean of uniform depth is researched theoretically by means of the homotopy analysis method (HAM), an analytic approximation method for nonlinear problems. Considering compressibility, a hydroacoustic wave can be produced by the interaction of two progressive gravity waves with the same wavelength travelling in opposite directions, which contains an infinite number of small denominators in the framework of the classical analytic approximation methods, like perturbation methods. Using the HAM, the infinite number of small denominators are avoided once and for all by means of choosing a proper auxiliary linear operator. Besides, by choosing a proper ‘convergence-control parameter’, convergent series solutions of the steady-state acoustic–gravity waves are obtained in cases of both non-resonance and exact resonance. It is found, for the first time, that the steady-state resonant acoustic–gravity waves widely exist. In addition, the two primary wave components and the resonant hydroacoustic wave component might occupy most of wave energy. It is found that the dynamic pressure on the sea bottom caused by the resonant hydroacoustic wave component is much larger than that in the case of non-resonance, which might even trigger microseisms of the ocean floor. All of these might deepen our understanding and enrich our knowledge of acoustic–gravity waves.

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Section: Resonant Wavessupporting

confidence: 67%

On the steady-state resonant acoustic–gravity waves

2018

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“…Note that (2.1) neglects the background compressibility of the static water column. This effect is important for the long range propagation of tsunamis, for example, but has been shown to be negligible for the acoustic modes of propagation; see Abdolali & Kirby (2017). The equation for pressure exerted by an elastic ice sheet on the underlying water column is given by Schulkes et al (1987),…”

Section: Governing Equationsmentioning

confidence: 99%

On the propagation of acoustic–gravity waves under elastic ice sheets

et al. 2018

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The propagation of wave disturbances in water of varying depth bounded above by ice sheets is discussed, accounting for gravity, compressibility and elasticity effects. Considering the more realistic scenario of elastic ice sheets reveals a continuous spectrum of acoustic–gravity modes that propagate even below the cutoff frequency of the rigid surface solution where surface (gravity) waves cannot exist. The balance between gravitational forces and oscillations in the ice sheet defines a new dimensionless quantity $\mathfrak{Ka}$. When the ice sheet is relatively thin and the prescribed frequency is relatively low ($\mathfrak{Ka}\ll 1$), the free-surface bottom-pressure solution is retrieved in full. However, thicker ice sheets or propagation of relatively higher frequency modes ($\mathfrak{Ka}\gg 1$) alter the solution fundamentally, which is reflected in an amplified asymmetric signature and different characteristics of the eigenvalues, such that the bottom pressure is amplified when acoustic–gravity waves are transmitted to shallower waters. To analyse these scenarios, an analytical solution and a depth-integrated equation are derived for the cases of constant and varying depths, respectively. Together, these are capable of modelling realistic ocean geometries and an inhomogeneous distribution of ice sheets.

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“…These assumptions are valid when the time periods are relatively short, and the corresponding phase speeds are low. It has been argued in various studies that the contributions of water compressibility and earth elasticity are vital not only for proper description of surface gravity waves 4–8 , but even more for waves travelling in the earth crust, such as P, S, Rayleigh and Love waves 9 , and acoustic-gravity waves that propagate in the water column 10–16 , or couple with the sea-floor 17 . The latter travel at speeds that far exceed the maximum tsunami phase speed carrying information on the fault geometry and dynamics 15 , and thus could be employed for early tsunami warning systems 18 and inverse models 19 , if analysed real-time.…”

Section: Introductionmentioning

confidence: 99%

“…Tsunami waves have been extensively studied in recent years, with attention focused on various physical features including thermal or salinity-based density stratification 6,20 , compressibility of the water column 4,6,8,15,20–24 , elastic deformation of the underlying solid earth 17,20,25 or combined effect of compressibility, stratification, and elasticity 26 . These studies confirmed, independently, that the time lag between model output and observations is sensitive to many of the physical features virtually neglected.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Water Compressibility, Sea-floor Elasticity, and Field Gravitational Potential on Tsunami Phase Speed

Abdolali

Kadri

Kirby

2019

Sci Rep

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Tsunamis can propagate thousands of kilometres across the ocean. Precise calculations of arrival times are essential for reliable early warning systems, determination of source and earth properties using the inverse problem, and time series modulation due to frequency dependency of phase speed. Far field observatories show a systematic discrepancy between observed and calculated arrival times. Models in present use and based on incompressible hydrodynamics and interaction with a rigid ocean floor overestimate the phase speed of tsunamis, leading to arrival time differences exceeding tens of minutes. These models neglect the simultaneous effects of the slight compressibility of water, sea-bed elasticity, and static compression of the ocean under gravity, hereinafter gravity. Here, we show that taking these effects into account results in more accurate phase speeds and travel times that agree with observations. Moreover, the semi-analytical model that we propose can be employed near real-time, which is essential for early warning inverse models and mitigation systems that rely on accurate phase speed calculations.

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Role of Compressibility on Tsunami Propagation

Cited by 33 publications

References 24 publications

On the steady-state resonant acoustic–gravity waves

On the steady-state resonant acoustic–gravity waves

On the propagation of acoustic–gravity waves under elastic ice sheets

Effect of Water Compressibility, Sea-floor Elasticity, and Field Gravitational Potential on Tsunami Phase Speed

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