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Acoustic tomography provides another approach to sens- ing the lower atmosphere based on interactions between the sound waves and turbulence. Because the travel time of acoustic signals depends on the temperature and wind velocity fields through which they propagate, the travel times along multiple transmission paths through a cross section of the atmosphere can be inverted to image the structure of those fields (Wilson and Thomson, 1994).
Another situation where the turbulence effects are important occurs when sound is refracted upward near the ground, as shown in Figure 5b. Refraction can sig- nificantly impact noise near highways, airports, factories, and wind turbines. When the sound propagates upwind or with a negative temperature gradient, upward refrac- tion occurs, which is beneficial from a noise mitigation perspective. In fact, at longer distances from the source (typically around several hundred meters), the upward refraction can create a shadow zone into which no sound energy penetrates according to ray acoustics.
However, in the 1980s and 1990s, as fully wave-based numerical methods for atmospheric sound propaga- tion were developed, it became apparent that even when diffraction into shadow zones was properly calculated, sound levels were still consistently underpredicted. Gil- bert et al. (1990) found that by including scattering from turbulence in the calculations, sound levels in the shadow dramatically increased, thus eliminating the bias. The scattering has other impacts such as smoothing interfer- ence patterns between the direct and ground reflection paths and between modes in near-ground waveguides for downwind propagation. An earlier Acoustics Today article by Wilson et al. (2015) discusses near-ground scat- tering and refraction effects, with example calculations and visualizations.
The third application is the impact of atmospheric turbu- lenceonpulsepropagation,suchasexplosionsandsonic booms (Figure 5c). On average, turbulence decreases the peak amplitude, increases the rise time, and elongates the tail of pulses. These effects tend to make sonic booms more tolerable to listeners (e.g., Stout et al., 2021) and are thus an important design consideration for “low- boom” supersonic aircraft, which involve shaping the airframe so as to tailor the characteristics waveform and perception of the boom. Turbulence is generally the strongest within the atmospheric boundary layer (ABL),
which extends from the ground up to about 200-3,000 m, depending on weather conditions. Strong turbulence can also occur at the interface between the ABL and the free troposphere above.
Last, there is the role of atmospheric turbulence in reducing acoustic signal coherence (Figure 5d). A pair of signals is said to be coherent when the amplitude and phase relationships between the signals are consistent. By randomizing the signal amplitude and phase as they propagate, turbulence reduces coherence when the sig- nals arrive at sensors (Ostashev and Wilson, 2015). The loss in coherence, which can occur over separations in space, time, and frequency, impacts the performance of outdoor acoustical systems. Many processing techniques, such as cross- correlation and beamforming, depend on high-signal coherence to provide high-resolution local- ization and boost the signal-to-noise ratio. Examples include “acoustic cameras” for accurately locating and identifying noise sources, gunfire and artillery direc- tion-finding systems (Costley, 2020), and ground-based microphone arrays for tracking aircraft.
Sound Propagation in a Fluctuating Ocean
Conceptually, sound propagation in a fluctuating ocean is similar to the atmosphere. However, there are specifics that confounded gaining an understanding of the topic first identified in the late 1940s amid the rapid develop- ment of naval applications after the war. A first-order understanding of weak fluctuations was not in place until the mid-1970s.
One of the main impediments was a misunderstanding and lack of measurements of ocean sound speed fine structure. For over a decade, misguided attempts were made to borrow treatments involving homogeneous iso- tropic turbulence from atmospheric WPRM.
The pioneering work of Garrett and Munk (1972) established that ocean fine structure was dominated by random fields of internal gravity waves that were inho- mogeneous and anisotropic; had their own intrinsic time evolution dictated by the dispersion relationship; and, most important, followed a “mostly” universal spectral form termed the Garrett-Munk (GM) spectrum (Spindel and Worcester, 2016). Internal gravity waves are similar to ocean surface waves created by the density difference between air and water; however, internal waves fill the
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