Weak Scattering of Sound Waves in Random Media That Have Arbitrary Power-Law Spectra

1999 ◽  
Author(s):  
D. K. Wilson
Keyword(s):  
Power Law ◽  
Random Media ◽  
Sound Waves ◽  
Arbitrary Power ◽  
Weak Scattering

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals Derivation of Lighthill’s Eighth Power Law of an Aeroacoustic Quadrupole in Acoustic Spacetime

Acoustics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 666-673
Author(s):  
Drasko Masovic ◽  
Ennes Sarradj
Keyword(s):  
Power Law ◽  
Sound Propagation ◽  
Dimensional Manifold ◽  
Sound Waves ◽  
Sound Generation ◽  
Speed Of Light ◽  
Acoustic Analogy ◽  
Analytical Treatment ◽  
Weak Perturbation ◽  
Generation Mechanisms

Acoustic spacetime is a four-dimensional manifold analogue to the relativistic spacetime with the reference speed of light replaced by the speed of sound. It has been established primarily for the indirect studies of relativistic phenomena by means of their better understood acoustic analogues. More recently, it has also been used for the analytical treatment of sound propagation in various uniform and non-uniform flows of the background fluid. In this paper the analogy is extended and utilized to derive Lighthill’s eight power law for sound generation of an aeroacoustic quadrupole. Adding to the existing analogue theory, propagating sound waves are described in terms of a weak perturbation of the background acoustic spacetime metric. The obtained result proves that the acoustic analogy can be extended to cover both weak perturbation of the fluid due to the sound waves and certain sound generation mechanisms, at least in incompressible low Mach number flows.

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