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Random focusing of nonlinear acoustic N-waves in fully developed turbulence: Laboratory scale experiment
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Image of FIG. 1.
FIG. 1.

(Color online) Sketch of the experimental setup (top view). Left photograph represents the spark source and the right photograph details the positions of the microphones (gray points) in the baffle.

Image of FIG. 2.
FIG. 2.

(a) Typical waveform measured in motionless air at a distance 210 mm from the spark source and (b) its time derivative.

Image of FIG. 3.
FIG. 3.

(Color online) (a) Distribution of normalized mean flow velocity 〈U〉/U jet; (b), (c) the intensities of turbulent fluctuations u rms/U mean, and v rms/U mean. Measurements were performed at a distance x 0 = 3.78 m from the nozzle with U jet = 40 m/s. Contour lines u rms/U mean = 0.28 and v rms/U mean = 0.24 denote the area where turbulence is statistically homogeneous and isotropic.

Image of FIG. 4.
FIG. 4.

(Color online) Comparison of the measured turbulence spectrum (jagged curve) with the modified von Kármán spectrum (smooth curve) and the Kolmogorov “−5/3” power law (solid line). Measurements were done at x 0 = 3.78 m on the jet axis with v rms = 3.4 m/s.

Image of FIG. 5.
FIG. 5.

(Color online) Spatial spectra of the longitudinal u (left) and transverse v (right) components of medium velocity fluctuations (jagged curves) measured at different points of the yz plane: (a), (b) at (x 0, 100, 0) mm, (c), (d) at (x 0, 500, 0) mm, and (e), (f) at (x 0, 720, 0) mm. Smooth curve—modified von Kármán spectrum; solid line—Kolmogorov’s −5/3 power law (v rms = 3.4 m/s).

Image of FIG. 6.
FIG. 6.

(Color online) Autocorrelation functions of the u component of the turbulent velocity field (v rms = 3.4 m/s) at (x 0, 0, 0) mm and (x 0, −350, 0) mm. Circles and diamonds indicate horizontal displacement and asterisks indicate vertical displacement, both along the y axis. Dashed-dotted, dashed, and solid curves are the corresponding fits.

Image of FIG. 7.
FIG. 7.

(Color online) Typical waveforms distorted by turbulence and measured at 2.19 m from the spark source. v rms = 2.5 m/s.

Image of FIG. 8.
FIG. 8.

(Color online) (a) Mean peak positive pressure, (b) mean rise time of the shock front, and (c) mean arrival time of the wave, as functions of the turbulence level v rms measured at r = 2.19 m. Vertical segments are the standard deviations. Individual measurements are shown with points.

Image of FIG. 9.
FIG. 9.

(a) Probability distributions of peak positive pressure and (b) rise time for various turbulence levels v rms at r = 2.19 m. Black curves represent fits of the peak pressure distributions using Eq. (5). The bin widths are 2 Pa and 0.5 μs, respectively. σp and σt are standard deviations.

Image of FIG. 10.
FIG. 10.

(Color online) Dependence of a and b coefficients in the generalized gamma distribution [Eq. (5)] on the turbulence level v rms.

Image of FIG. 11.
FIG. 11.

(Color online) (a) Dependence of the mean peak positive pressure, and (b) the mean rise time on the distance of propagation in turbulent air. Vertical bars show the standard deviation, σp and σt .


Generic image for table

Mean flow velocity U mean measured on axis at x 0 = 3.78 m, rms values of the fluctuating velocity u rms and v rms, and distance to the first caustic r caust [see Eq. (4)] as a function of the jet nozzle velocity U jet.

Generic image for table

Comparison of spatial and time scales of the sonic boom problem with the laboratory scale experiment.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Random focusing of nonlinear acoustic N-waves in fully developed turbulence: Laboratory scale experiment