Covariance Properties of Waves Propagating in a Random Medium

Chen, K. K.; Soong, T. T.

doi:10.1121/1.1912542

Cited by 21 publications

(4 citation statements)

References 1 publication

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“…These conclusions are similar to those already known for linear waves through a medium with a weakly random index of refraction, e.g. Chen & Soong (1971) and Garnier (2001b, p. 151).…”

Section: A Steady Train Of Attenuated Stokes Wavessupporting

confidence: 91%

Weakly nonlinear surface waves over a random seabed

Mei

Hancock

2003

J. Fluid Mech.

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We study the effects of multiple scattering of slowly modulated water waves by a weakly random bathymetry. The combined effects of weak nonlinearity, dispersion and random irregularities are treated together to yield a nonlinear Schrödinger equation with a complex damping term. Implications for localization and side-band instability are discussed. Transmission and nonlinear evolution of a wave packet past a finite strip of disorder is examined.

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“…These conclusions are similar to those already known for linear waves through a medium with a weakly random index of refraction, e.g. Chen & Soong (1971) and Garnier (2001b, p. 151).…”

Section: A Steady Train Of Attenuated Stokes Wavessupporting

confidence: 91%

Weakly nonlinear surface waves over a random seabed

Mei

Hancock

2003

J. Fluid Mech.

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“…[3], can be applied for heterogeneous media, however its solution is very challenging. The scale of the difficulties to overcome is seen in [12,13].…”

Section: Discussionmentioning

confidence: 99%

“…Therefore the influence of heterogeneity is taken into account by 1 k in Eq. (12). Equation ( 14) for 1 k may be transformed to Considerable attenuation is explained by the accumulation of the dispersion effects.…”

Section: The Aforementioned Assumptionmentioning

confidence: 99%

Propagation of Random Waves in Elastic Media with Microheterogeneities

Belyaev

2012

KEM

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Propagation of elastic waves in heterogeneous linear 1-D media is considered. The scalar wave equation is transformed by the Liouville substitution and the Dyson integral equation is applied for a statistically homogeneous field of heterogeneities. The result is the mean wave field which is analysed in detail for the exponential correlation functions. The general case of the random elastic medium with an arbitrary heterogeneity of small scale is considered and simple closed form expressions for the mean field and attenuation are derived.

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“…In fact, Wenzel [34], Sobczyk, Wedrychowicz and Spencer [35], Frankenthal and Beran [36], Uscinski [37] and Frisch [38] have made extensive studies on various aspects of randomness in physical sciences, wave propagation phenomena and random characteristics of media. In particular, Chen and Soong [39] worked on covariance properties of waves propagating in a medium. A detailed discussion on properties and applications of random differential equations can be found, among others, in the treatise of Soong [40].…”

Section: Introductionmentioning

confidence: 99%

On wave propagation in a random micropolar generalized thermoelastic medium

Mitra

Bhattacharyya

2017

Archives of Thermodynamics

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This paper endeavours to study aspects of wave propagation in a random generalized-thermal micropolar elastic medium. The smooth perturbation technique conformable to stochastic differential equations has been employed. Six different types of waves propagate in the random medium. The dispersion equations have been derived. The effects due to random variations of micropolar elastic and generalized thermal parameters have been computed. Randomness causes change of phase speed and attenuation of waves. Attenuation coefficients for high frequency waves have been computed. Second moment properties have been briefly discussed with application to wave propagation in the random micropolar elastic medium. Integrals involving correlation functions have been transformed to radial forms. A special type of generalized thermo-mechanical auto-correlation functions has been used to approximately compute effects of random variations of parameters. Uncoupled problem has been briefly outlined.

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Covariance Properties of Waves Propagating in a Random Medium

Cited by 21 publications

References 1 publication

Weakly nonlinear surface waves over a random seabed

Weakly nonlinear surface waves over a random seabed

Propagation of Random Waves in Elastic Media with Microheterogeneities

On wave propagation in a random micropolar generalized thermoelastic medium

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