Turbulent spectral broadening of backscattered acoustic pulses

Abstract

The analysis studies the broadening of the frequency spectrum of an acoustic plane-wave pulse backscattered into a finite-angle receiver by the action of a transverse mean wind which moves turbulent velocity and temperature fluctuations through the beam. The results include the frequency spectrum I(k) of the acoustic pressure as a function of wavenumber and the spectral equivalent width b, as a function of mean transverse wind speed and receiver aperture. For broad beams, both temperature and velocity fluctuations contribute to the apparent 180°-backscatter intensity, and the contributing eddy scales vary from λ/2 to λ/√2. Again for broad beams and for typical experimental parameters for atmospheric echosondes, the broadening effects of mean transverse wind in the scattering volume outweigh the broadening effects of turbulence trransported by a mean transverse wind during propagation to the scattering volume. However, as the receiver beam angle decreases, the spectral broadening drops to zero, regardless of mean wind. Figures are included to show the effects of wind broadening for the case of intermediate receiver beam angles.

Numerical assessment of the scattering of acoustic waves by turbulent structures

“…where H (2) m is the m th order Hankel function of the second kind. If the observer is chosen very far from the vortex, an asymptotic expression of the Hankel function can be used and the pressure expression in Eq.…”

Some recent NOAA theoretical work on echo sounding in the atmosphere

“…Similarly, if the echosonde uses a pulse of half-length l, the thickness of the shell varies from l at the zenith to 21 at the horizon. Recently, Brown [1974] found that the eddy scale parallel to the direction between differential scattering to element and the receiver varies from the expected 2,/2 at the zenith to 2,/(2) •/: at the horizon, and that the corresponding traverse scales vary from the outer scale Lo at the zenith to 2, at the horizon. Since the angle that a wind transverse to the echosonde axis makes with the above direction to a scattering element also varies with elevation, the total effect on the broadening of the frequency spectrum becomes quite complicated.…”

“…Their result implies that most of the material in Tatarskii's monographs applies to sound propagation in both audible and high-frequency ranges. The present paper reviews some recent work by Brown [1972Brown [ , 1974 number of the transverse wind, FA(•, 0) is the two-dimensional spatial spectrum of th e amplitude fluctuations [see Clifford and Brown, 1971] over the transverse Fourier space with the coordinates K,, a = 1, 2, and The remarks on the convenient effect that the stationarity condition has on the form of the forwardscatter amplitude spectrum apply equally to the spectral density of the intensity l(k). Writing Ak = k -ko as before, Brown and Clifford [1973b]…”

Spectral broadening of acoustic waves by convected vortices

“…This model includes the effect of multiple scattering that can appear if the turbulent volume is large enough so that acoustic waves are scattered successively by numerous eddies, while previous models were restricted to the hypothesis of single scattering (usually using the Born approximation). Brown (1974) and Brown & Clifford (1973, 1976) developed an analytical model for the scattered intensity based on an inhomogeneous Helmholtz equation with a source term involving velocity and temperature fluctuations. The parabolic equation has been used to derive both analytical (Ostashev et al 2001) and numerical (Dallois et al 2001) models for the evolution of the sound pressure level with the propagation distance through turbulence.…”