Acoustic Length Scale Research Articles

Infrasound scattering from stochastic gravity wave packets

Long-range infrasound propagation problems are characterized by a large number of length scales and a large number of propagating modes. In the atmosphere, these modes are confined within waveguides causing the sound to propagate through multiple paths to the receiver. In most infrasound modeling studies, the small scale fluctuations are represented as a “frozen” gravity wave field that is superimposed on a given average background state, and the normal modes are obtained using a single calculation. Direct observations in the lower stratosphere show, however, that the gravity wave field is very intermittent, and is often dominated by rather well defined large-amplitude wave packets. In the present work, we use a few proper modes to describe both the gravity wave field and the acoustic field. Owing to the disparity of the gravity and acoustic length scales, the acoustic field can be constructed in terms of asymptotic expansions using the method of multiple scales. The amplitude evolution equation involves random terms that can be related to vertically distributed gravity wave sources. To test the validity of the theory, numerical results are compared with recorded signals. It is shown that the present stochastic theory offers significant improvements over current semi-empirical approaches.

Dynamics of an elastic sphere containing a thin creeping region and immersed in an acoustic region for similar viscous-elastic and acoustic time and length scales

The characteristic time of low-Reynolds-number fluid–structure interaction scales linearly with the ratio of fluid viscosity to solid Young’s modulus. For sufficiently large values of Young’s modulus, both time and length scales of the viscous-elastic dynamics may be similar to acoustic time and length scales. However, the requirement of dominant viscous effects limits the validity of such regimes to micro-configurations. We here study the dynamics of an acoustic plane wave impinging on the surface of a layered sphere, immersed within an inviscid fluid, and composed of an inner elastic sphere, a creeping fluid layer and an external elastic shell. We focus on configurations with similar viscous-elastic and acoustic time and length scales, where the viscous-elastic speed of interaction between the creeping layer and the elastic regions is similar to the speed of sound. By expanding the linearized spherical Reynolds equation into the relevant spectral series solution for the hyperbolic elastic regions, a global stiffness matrix of the layered elastic sphere was obtained. The maximal pressure difference induced by the acoustic wave on the creeping region was found to occur for identical viscous-elastic and acoustic length scales. Comparing an elastic sphere with an embedded creeping layer to a fully elastic sphere, a significant reduction in magnitude and fluctuations (with regard to wavelength) are observed for both the displacements of the solid and target strength of the sphere. This effect was most significant for identical viscous-elastic and acoustic time scales. This work relates viscous-elastic dynamics to acoustic scattering and may pave the way to the design of novel metamaterials with unique acoustic properties.

On resonant triad interactions of acoustic–gravity waves

The propagation of wave disturbances in water of uniform depth is discussed, accounting for both gravity and compressibility effects. In the linear theory, free-surface (gravity) waves are virtually decoupled from acoustic (compression) waves, because the speed of sound in water far exceeds the maximum phase speed of gravity waves. However, these two types of wave motion could exchange energy via resonant triad nonlinear interactions. This scenario is analysed for triads comprising a long-crested acoustic mode and two oppositely propagating subharmonic gravity waves. Owing to the disparity of the gravity and acoustic length scales, the interaction time scale is longer than that of a standard resonant triad, and the appropriate amplitude evolution equations, apart from the usual quadratic interaction terms, also involve certain cubic terms. Nevertheless, it is still possible for monochromatic wavetrains to form finely tuned triads, such that nearly all the energy initially in the gravity waves is transferred to the acoustic mode. This coupling mechanism, however, is far less effective for locally confined wavepackets.

On simulation of sonic‐boom propagation with realistic modeling of the atmospheric turbulence

The propagation of sonic booms is from high above the ground to ground level, and over the path the dominant acoustic length scales in the signatures fall within what is known as the inertial subrange, for which there is a considerable body of basic theoretical knowledge. Any model of boom–turbulence interaction that requires a value for an outer scale has very weak theoretical basis. However, the range of turbulence scales within the inertial subrange is huge and different scales have different effects. The present paper argues that the turbulence can be split in a well‐defined and logical manner, with the resulting scale at which the split occurs serving as an outer scale with respect to the turbulence that affects the rise times of sonic booms. Although molecular relaxation accounts for a substantial fraction of the rise times, the bulk of the thickening during daytime overflights is associated with turbulence. A theory for such thickening that simultaneously took both nonlinear steepening and turbulence into account had been proposed in the early 1970s by Plotkin and George, but had been criticized for its dependence on the choice of an outer scale. The proposed partitioning removes this objection and combines the salient ideas of Plotkin and George with others proposed by the author during the same epoch for the effects of inertial‐subrange‐scale turbulence on rise times.

Nonlinear viscous effects arising near a boundary discontinuity

The problem of nonlinear viscous flow generated by an acoustic wave traveling in proximity to a rigid boundary having a rapid variation in shape will be examined. Special attention will be given to the problems of acoustic streaming and instability in the Stokes boundary layer. The acoustic particle velocity amplitude for which instability is observed corresponds to the case where η2R1/2/S2 = O(1). Below this amplitude threshold, acoustic waves generate time‐average motion which is called acoustic streaming. Preliminary results show that the boundary geometry plays a major part in the instability mechanism in that an inflection point in the wall geometry gives rise to a bifurcation point according to linear theory. This state of affairs is in marked contrast to Stokes layers generated over flat boundaries, which exhibit no such bifurcation point. By virtue of the compressible character of the base flow, the characteristic acoustic scale (namely, the acoustic wavelength) does influence the spatial development for the vortical disturbance field. Therefore, an analysis of the relative influence of geometric and acoustic length scales in the development of the distribution field will also be presented.