On the use of evanescent plane waves for low-frequency energy transmission across material interfaces

Abstract

The transmission of airborne sound into high-impedance media is of interest in several applications. For example, sonic booms in the atmosphere may impact marine life when incident on the ocean surface, or affect the integrity of existing structures when incident on the ground. Transmission across high impedance-difference interfaces is generally limited by reflection and refraction at the surface, and by the critical angle criterion. However, spatially decaying incident waves, i.e., inhomogeneous or evanescent plane waves, may transmit energy above the critical angle, unlike homogeneous plane waves. The introduction of a decaying component to the incident trace wavenumber creates a nonzero propagating component of the transmitted normal wavenumber, so energy can be transmitted across the interface. A model of evanescent plane waves and their transmission across fluid-fluid and fluid-solid interfaces is developed here. Results are presented for both air-water and air-solid interfaces. The effects of the incident wave parameters (including the frequency, decay rate, and incidence angle) and the interfacial properties are investigated. Conditions for which there is no reflection at the air-solid interface, due to impedance matching between the incident and transmitted waves, are also considered and are found to yield substantial transmission increases over homogeneous incident waves.

Martian Infrasound: Numerical Modeling and Analysis of InSight's Data

“…Two main types of air-to-ground conversion coexist: classical acoustic wave to seismic wave transmission (Aki & Richards, 2002) and compliance effects (Kenda et al, 2017;Sorrells, 1971;Sorrells et al, 1971). A smooth transition links the two (Woods et al, 2015). Additionally, studying the ground displacements caused by infrasonic waves enables one to constrain the subsurface below the InSight lander.…”

Bounded inhomogeneous wave profiles for increased surface wave excitation efficiency at fluid–solid interfaces

“…This work extends that of Vanaverbeke et al, 22 who demonstrated that bounded inhomogeneous waves improve the surface wave excitation efficiency as compared to Gaussian and square waves, by examining the effect of tuning the decay parameter. It was shown here that the minimum in the plane wave reflection coefficient with respect to the decay parameter 23,24 provides a good prediction of the minimum in the local reflection coefficient for bounded wave profiles, which is exact in the limit of large beamwidths. Inhomogeneous plane wave theory also provides an indication of the decay parameter value which maximizes the surface wave excitation efficiency, but this value is sensitive to the beamwidth of bounded waves and there is generally a shift to larger decay parameter values due to the greater spatial concentration of the incident wave energy at those larger decay rates.…”

“…For the plane wave, the decay parameter gives the rate of exponential decay perpendicular to the propagation direction. 23,30,31 As is evident, the form of the plane wave reflection coefficient, including the location of the minimum, is closely matched by the local reflection coefficients for the wider beamwidths. The decay parameter which yields the minimum for the profile with the half beamwidth W ¼ 30 mm is b ¼ 110:8 rad/m, which gives a 0:18% error with respect to the value for the plane incident wave, b ¼ 111:0 rad/m.…”

“…where b is the decay parameter, W is the half beamwidth, p is the steepness parameter, x is the angular frequency, t is the time variable, andà is the wave potential amplitude. This versatile form of the profile not only allows for an exponentially decaying term that is analogous to the decay of inhomogeneous plane waves perpendicular to the propagation direction, 23,30,31 but it also facilitates the modeling of other waveforms, including Gaussian and square profiles. 22 Note that the term "bounded" is used to describe profiles of this type since the amplitude takes on very small values outside of the spatial region near x 0 ¼ 0, a spatial windowing which is controlled by the term e Àð1=pÞðjx 0 j=WÞ p in Eq.…”

“…More importantly, it was shown that the surface wave excitation efficiency for the bounded inhomogeneous incident waves was substantially higher than that for Gaussian and square profiles. Interestingly, previous work has shown that, by tuning the decay rate of incident inhomogeneous plane waves, a zero of the reflection coefficient can be achieved near the Rayleigh angle for lossless fluid-solid interfaces, 23 and near-zero values can be achieved for low-loss, viscoelastic fluid-solid interfaces. 24 Though Vanaverbeke et al, 22 along with others, 13,21,25,26 have given a detailed account of the effects of the frequency, beamwidth, and steepness of the incident profiles, they have not reported tuning the decay parameter to improve the surface wave excitation efficiency.…”