Multiscale Analysis of Spectral Broadening of Acoustic Waves by a Turbulent Shear Layer

Garnier, Josselin; Gay, Etienne; Savin, Éric

doi:10.1137/19m1276492

Cited by 2 publications

(2 citation statements)

References 23 publications

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“…Now (37) shows that if the ambient medium is frozen (i.e., independent of t), then the wave frequency is unchanged, as expected. Alternatively, a time-dependent ambient medium is responsible for the spectral broadening, or "haystacking," effect of the acoustic spectrum around a tone frequency [12,13,15,24,27]. Spatial variations of the ambient flow velocity and sound speed are responsible for the phase shift effect [31], which is manifested in the evolution of the wave vector k along the paths.…”

Section: Evolution Propertiesmentioning

confidence: 99%

“…ε n dp (2π) n f (εp) φ(k − p) , and thereforeP (x, εD x )f x ε φ(x) = R n dk (2π) n e ix•k P (x, εk) f n e ix•k P (x, εk) R n ε n dp (2π) n f (εp) φ(k − p) = R n dk (2πε) n e i x ε •k P (x, k) y ε •(k−p) φ(y)dy = R n e −i( x ε −y)•(k−p) φ(x − εy)ε n dy ,so that one finally hasP (x, εD x )f n e i x ε •k P (x, k) R n dp (2π) n f (p) R n x ×R n y e −i( x ε −y)•(k−p) φ(x−εy)ψ(x)ε n dydx = n e i x ε •p f (p)W ε [φ, ψ](x, k − p) ,which when identified with (78) gives the claimed result. Regarding(24), it now suffices to observe thatW ε f x ε P (x, εD x )φ, ψ = R n dp (2π) n e i x ε •p f (p)W ε [P (x, εD x )φ, ψ](x, k − p) = R n dp (2π) n e i x ε •p f (p)P (x, k − p)W ε [φ, ψ](x, k − p) + O(ε) ,…”

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confidence: 99%

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Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows

Akian¹,

Savin²

2021

Multiscale Model. Simul.

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We study the propagation of sound waves in a three-dimensional, infinite ambient flow with weak random fluctuations of the mean particle velocity and speed of s ound. We more particularly address the regime where the acoustic wavelengths are comparable to the correlation lengths of the weak inhomogeneities-the so -called we ak co upling li mit. Th e an alysis is ca rried on st arting from the linearized Euler equations and the convected wave equation with variable density and speed of sound, which can be derived from the nonlinear Euler equations. We use a multiscale expansion of the Wigner distribution of a velocity potential associated to the waves to derive a radiative transfer equation describing the evolution of the angularly resolved wave action in space/time phase space. The latter experiences convection, refraction, and scattering when it propagates through the heterogeneous ambient flow, a lthough t he overall wave a ction i s c onserved. T he c onvection and refraction phenomena are accounted for by the convective part of the transport equation and depend on the smooth variations of the ambient quantities. The scattering phenomenon is accounted for by the collisional part of the transport equation and depends on the cross-power spectral densities of the fluctuations o f t he a mbient q uantities a t t he w avelength s cales. T he r efraction, p hase shift, spectral broadening, and multiple scattering effects of the high-frequency regimes described in various previous publications are thus encompassed by the proposed model. The overall derivation is based on the interpretation of spatial-temporal Wigner transforms in terms of semiclassical operators in their standard quantization.

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Section: Evolution Propertiesmentioning

confidence: 99%

mentioning

confidence: 99%

Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows

Akian¹,

Savin²

2021

Multiscale Model. Simul.

Self Cite

View full text Add to dashboard Cite

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Wave propagation in random two-dimensional turbulence: a multiscale approach

Resseguier,

Hascoët,

Chapron

2024

J. Fluid Mech.

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To study two-dimensional dispersive waves propagating through turbulent flows, a new and less restrictive fast waves approximation is proposed using a multiscale setting. In this ansatz, large and small scales of the turbulence are treated differently. Correlation lengths of the random small-scale turbulence components can be considered negligible in the wave packet propagating frame. Nevertheless, the large-scale flow can be relatively strong, to significantly impact wavenumbers along the propagating rays. New theoretical results, numerical tools and proxies are derived to describe ray and wave action distributions. All model parameters can be calibrated robustly from the large-scale flow component only. We illustrate our purpose with ocean surface gravity waves propagating in different types of surface currents. The multiscale solution is demonstrated to efficiently document wave trapping effects by intense jets.

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Multiscale Analysis of Spectral Broadening of Acoustic Waves by a Turbulent Shear Layer

Cited by 2 publications

References 23 publications

Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows

Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows

Wave propagation in random two-dimensional turbulence: a multiscale approach

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