Acoustic emissions from convected wave packets

Abstract

Localized acoustic sources can often be modeled by wave packets. It has been recognized for a long time that the particular structure of these wave packet sources has a strong influence on the character of the acoustic emission to the far field. In the present work, we study the acoustic emission patterns with respect to the phase velocity, group velocity, size, and aspect ratio of the wave packet sources. To this end, the acoustic problem is formulated on the basis of Lighthill's acoustic analogy and then recast to the geometrical problem of conic sections. This leads to the notion of elliptic ͑subsonic͒, parabolic ͑sonic͒, and hyperbolic ͑supersonic͒ acoustic emission patterns. The resulting geometric theory for acoustic emissions from wave packets includes phenomena such as Mach waves, bi-and superdirectivity, Doppler shift, and silent directions.

Linear stability and acoustic characteristics of compressible, viscous, subsonic coaxial jet flow

“…In the (ω, α r , β) space, the acoustic dispersion relation can be represented by a double cone, which is symmetric with respect to the origin. 10 To show that the acoustic eigenmodes indeed satisfy Eq. (10) the dominant radial wavenumber β * of an eigenmode can also be computed by applying a Hankel transform 39 to the corresponding eigenfunction in the radial direction:p…”

“…By using concepts from acoustic theory, [8][9][10] the acoustic modes can be assigned to specific radiation angles with respect to the jet axis. Analyzing the disturbance eigenfunctions proves to be essential for the understanding of the directivity of the noise emissions.…”

The influence of a pressure wavepacket's characteristics on its acoustic radiation

“…Expression (9) shows that the acoustic response toward the direction h in the far-field is proportional to the amplitude of the spatial mode K ¼ k a cos h. Thus jKj k a , meaning that only those spatial modes of the pressure distribution with a wavenumber smaller than k a ¼ M c k h are able to excite the acoustic far-field. They have thus been called the supersonic tail of the wavepacket, for their phase velocity x/K is faster than the sound speed.…”

“…It has been carried out by Obrist 8 who modeled the first component of the Lighthill tensor as a wavepacket, and investigated the role of its phase velocity and its spatial distribution in a multidimensional space, then extending to that of the group velocity. 9 That author emphasized the predominant effects of those characteristics on directivity patterns. The same formalism has been used through analytical and experimental work by Papamoschou 10 and Cavalieri et al 11 For jittering wavepackets in a middle subsonic flow, the temporal fluctuations of the envelope highlighted efficient conditions for sound radiation.…”

“…The same track was followed by Fleury et al 18 on a cylindrical Kirchhoff surface in the context of round jet noise. The acoustic energy radiated by a pressure distribution is triggered by its modes in the wavenumber spectrum lower than the acoustic wavenumber (supersonic phase speed 9,15,19,20 ). The localized spatial envelope yields an amplitude modulation in the wavenumber spectrum, instead of a single pic at the hydrodynamic wavenumber in the case of a wave without space modulation.…”