Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows
Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows
复制标题
随机非均质流中声波多次散射的动力学模型
DOI：
10.1137/20m1370495
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
É. Savin
中科院分区：
文献类型：
--
作者：
J. Akian;É. Savin
我们研究了声波在三维无限大环境流中的传播，其中平均粒子速度和声速具有微弱的随机波动。我们更特别地解决的制度，其中的声波波长是可比的弱不均匀性的相关长度-所谓的弱耦合限制。从线性化的欧拉方程和由非线性欧拉方程导出的变密度、变声速的对流波动方程出发进行了分析。我们使用的Wigner分布的多尺度扩展的速度势相关的波导出的辐射传输方程描述的演化的角度分辨波的作用在空间/时间相空间。后者经历对流，折射和散射时，它通过非均匀的环境流传播，虽然整体波的作用是保守的。对流和折射现象由输运方程的对流部分来解释，并取决于环境量的平滑变化。散射现象是占碰撞部分的传输方程，并取决于交叉功率谱密度的波动的环境量在波长尺度。折射，相移，光谱展宽，和多次散射的影响，在以前的各种出版物中描述的高频制度，因此所提出的模型。整体推导基于根据半经典算子的时空维格纳变换的解释，沿着与Bal [Wave Motion 43，132-157（2005）]和Baydoun等人[Wave Motion 51，1325-1348（2014）]相同的线。
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 sound. We more particularly address the regime where the acoustic wavelengths are comparable to the correlation lengths of the weak inhomogeneities--the so-called weak coupling limit. The analysis is carried on starting 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 multi-scale 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, although the overall wave action is conserved. The convection 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 of the ambient quantities at the wavelength scales. The refraction, phase 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, along the same lines as Bal [Wave Motion 43, 132-157 (2005)] and Baydoun et al. [Wave Motion 51, 1325-1348 (2014)].