Caustic diffraction fields in a downward refracting atmosphere

Salomons, Erik M.

doi:10.1121/1.423966

Cited by 10 publications

(8 citation statements)

References 37 publications

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“…This time, the focal zone moves towards the right and the caustic curve remains close to the ground. This explains why the additional contribution at ground level is of larger amplitude for the second focal zone, as the decay of a signal away from a caustic is related to the distance from the caustic [see, e.g., Salomons (1998)].…”

Section: B Hillmentioning

confidence: 99%

Characterization of topographic effects on sonic boom reflection by resolution of the Euler equations

Emmanuelli

Dragna

Ollivier

et al. 2021

The Journal of the Acoustical Society of America

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The influence of topography on sonic boom propagation is investigated. The full two-dimensional Euler equations in curvilinear coordinates are solved using high-order finite-difference time-domain techniques. Simple ground profiles, corresponding to a terrain depression, a hill, and a sinusoidal terrain, are examined for two sonic boom waves: a classical N-wave and a low-boom. Ground reflection of the sonic boom is affected by elevation variations: a concave ground profile induces compression, which tends to increase the peak pressure in particular, while the opposite is true for convex elevation variations, which lead to expansion and a reduction in peak pressure. The reflected boom is then strongly altered. Furthermore, a sufficiently concave topography can cause focal zones, which generate extra contributions at ground level in the form of U-waves in addition to the reflected wave. This mechanism has the largest effect on waveforms at ground level. The variations of standard metrics are of a few dBs compared to a flat ground for both sonic boom waves, and they are notably greater for the terrain depression than for the hill. Finally, in the case of a sinusoidal terrain, the pressure waveforms are composed of multiple arrivals due to successive focal zones.

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Section: B Hillmentioning

confidence: 99%

Characterization of topographic effects on sonic boom reflection by resolution of the Euler equations

Emmanuelli

Dragna

Ollivier

et al. 2021

The Journal of the Acoustical Society of America

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“…Signals travelling in the atmosphere undergo a phase shift when grazing a caustic, so that an initially N-shaped waveform, typical of an explosive source, is transformed into a U-wave (Rogers & Gardner 1980;Pierce 1985;Marchiano, Coulouvrat & Grenon 2003). Diffraction at a caustic also plays an important role, especially for low-frequency waves (Pierce 1985;Salomons 1998;Marchiano et al 2003). The atmospheric stratification imposed by the gravity force has a considerable impact on acoustic propagation.…”

Section: Physical Phenomena Affecting Infrasound Propagationmentioning

confidence: 99%

Three-dimensional direct numerical simulation of infrasound propagation in the Earth’s atmosphere

et al. 2018

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A direct numerical simulation of the three-dimensional unsteady compressible Navier–Stokes equations is performed to investigate the infrasonic field generated in a realistic atmosphere by an explosive source placed at ground level. To this end, a high-order finite-difference method originally developed for aeroacoustic applications is employed. The maximum overpressure and the main frequency of the signal recorded at 4 km distance from the source location are about 4000 Pa and 0.2 Hz, respectively. The atmosphere is parametrized as a vertically stratified medium, constructed by specifying vertical profiles of the temperature and the horizontal wind which reproduce measurements. The computation is carried out up to 140 km altitude and 450 km range. The goal of the present paper is twofold. On the one hand, the feasibility of using a direct numerical simulation of the three-dimensional fluid dynamic equations for the detailed description of long-range propagation in the atmosphere is proven. On the other hand, a physical analysis of the infrasonic field is realized. In particular, great attention is directed towards some important phenomena which are not taken into account or not well predicted by classical propagation models. To begin with, the present study clearly demonstrates that the weakly nonlinear ray theory may lead to an incorrect evaluation of the waveform distortion of high-amplitude waves propagating towards the lower thermosphere. In addition, signals recorded in the shadow zones are investigated. In this regard, the influence on the acoustic field of temperature and wind inhomogeneities of length scale comparable with the acoustic wavelength is analysed. The role of diffraction at the thermospheric caustic is finally examined and it is pointed out that the amplitude of the source may have a strong impact on the length of the shadow zone.

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“…In such systems, the consecutive effect of weak scattering events that are correlated in space leads to strong focusing in branch-like patterns, connected to the formation of random caustics, which are regions where the flow is focused. Examples of this phenomenon include the random focusing of electrons in semiconductors [8,[21][22][23][24] and microwaves propagating in cavities with weak scatterers [9], as shown in Fig.1.2, and it is considered to explain the twinkling of starlight due to its propagation through the slightly inhomogeneous atmosphere [25][26][27][28][29], as well as the focusing of sound waves in the ocean due to water density variations [30][31][32][33][34][35][36]. All those phenomena can be modeled using Schrödinger-type equations, which can then be studied using Hamiltonian rays.…”

Section: 0mentioning

confidence: 99%

Random focusing of tsunami waves

et al. 2015

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Branched flow is a universal phenomenon of random focusing that occurs in wave or particle flows that propagate in weakly scattering, correlated random media. The consecutive effect of small random forces leads to regions of strong focusing which have the appearance of branches and originate from the formation of random caustics. This phenomenon has been experimentally and theoretically studied in various systems, ranging from experimental observations in electronic microdevices on the micrometer scale to theoretical predictions for the propagation of sound waves in the ocean, on the scale of thousands of kilometers. Reconstructions of the tsunami of March 2011 exhibited strong fluctuations in the tsunami height, associated with a filamentation of the flow, reminiscent of the structures observed for example in electron flows in semiconductor microstructures. This raises the question, to what extent are the same mechanisms at play in these very different physical systems and what impact do they have for tsunami predictions. Developing a theory of random caustics and branching in tsunami waves is the main purpose of this thesis.We will start by showing that tsunamis indeed exhibit strong focusing even when propagating over a weakly scattering region of the ocean floor. We will therefore develop the stochastic theory for the characteristic length scale on which random caustics appear in the propagations of tsunamis described by ray equations. We then confirm that the focusing regions of tsunami waves follow the scaling predicted by stochastic ray dynamics with respect to the parameters of the bathymetry. We thus show that tsunamis are indeed subject to the phenomenon of branched flow. We will furthermore demonstrate that, due to the fact that already tiny bathymetry fluctuations can be a source of branched flow, bathymetry has a severe impact on the predictability of tsunami heights. Small uncertainties in the knowledge of the ocean's bathymetry can lead to drastically wrong predictions.Because the ocean floor bathymetry is known to exhibit anisotropies and to be correlated on several length scales due to the various geological processes contributing to its formation, we later extend the general theory of branched flows to systems where the random medium is correlated on more than one single length-scale, both for tsunami waves and Hamiltonian rays, as it is also relevant to many other systems. We calculate how such correlations affect the typical length scale of branching. Our theory is then applicable to a large variety of correlation functions, either anisotropic or isotropic with multiple correlation lengths. We conclude with a proposal for an experiment which scales a tsunami event down to the size of a tank in a laboratory to study the focusing effect of bathymetry structures. Such a tool could be useful in tsunami studies and forecasting and it would allow us to experimentally verify our theoretical and numerical results on random focusing of tsunami waves.3

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Caustic diffraction fields in a downward refracting atmosphere

Cited by 10 publications

References 37 publications

Characterization of topographic effects on sonic boom reflection by resolution of the Euler equations

Characterization of topographic effects on sonic boom reflection by resolution of the Euler equations

Three-dimensional direct numerical simulation of infrasound propagation in the Earth’s atmosphere

Random focusing of tsunami waves

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