×

zbMATH — the first resource for mathematics

Wavepackets in the velocity field of turbulent jets. (English) Zbl 1291.76280
Summary: We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers \(m\) ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10%, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers \(0. 3\leqslant St\leqslant 0. 9\) and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

MSC:
76Q05 Hydro- and aero-acoustics
76F40 Turbulent boundary layers
76-05 Experimental work for problems pertaining to fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1017/jfm.2012.247 · Zbl 1246.76005 · doi:10.1017/jfm.2012.247
[2] DOI: 10.2514/3.12173 · Zbl 0825.76286 · doi:10.2514/3.12173
[3] DOI: 10.1146/annurev-fluid-011212-140756 · Zbl 1359.76257 · doi:10.1146/annurev-fluid-011212-140756
[4] DOI: 10.1017/S0022112081000608 · doi:10.1017/S0022112081000608
[5] DOI: 10.1017/S0022112084000124 · Zbl 0543.76109 · doi:10.1017/S0022112084000124
[6] DOI: 10.1063/1.3555634 · Zbl 06421675 · doi:10.1063/1.3555634
[7] DOI: 10.1146/annurev.fluid.29.1.245 · doi:10.1146/annurev.fluid.29.1.245
[8] DOI: 10.1017/S0022112006001613 · Zbl 1104.76023 · doi:10.1017/S0022112006001613
[9] DOI: 10.1017/S002211200700612X · Zbl 1116.76073 · doi:10.1017/S002211200700612X
[10] DOI: 10.1017/jfm.2011.401 · Zbl 1241.76203 · doi:10.1017/jfm.2011.401
[11] DOI: 10.1017/S0022112010002375 · Zbl 1205.76242 · doi:10.1017/S0022112010002375
[12] DOI: 10.1017/S0022112068000248 · doi:10.1017/S0022112068000248
[13] DOI: 10.2514/3.60978 · doi:10.2514/3.60978
[14] Boundary-Layer Theory (1979)
[15] DOI: 10.1017/S0022112062001421 · Zbl 0118.21102 · doi:10.1017/S0022112062001421
[16] DOI: 10.1016/0022-460X(79)90573-X · doi:10.1016/0022-460X(79)90573-X
[17] DOI: 10.1121/1.1909297 · doi:10.1121/1.1909297
[18] DOI: 10.1017/S0022112071001745 · doi:10.1017/S0022112071001745
[19] DOI: 10.1016/S0142-727X(00)00021-7 · doi:10.1016/S0142-727X(00)00021-7
[20] DOI: 10.2514/3.60743 · doi:10.2514/3.60743
[21] DOI: 10.1017/S0022112076002176 · Zbl 0338.76021 · doi:10.1017/S0022112076002176
[22] DOI: 10.1017/S0022112088002939 · doi:10.1017/S0022112088002939
[23] DOI: 10.1017/S0022112087000624 · doi:10.1017/S0022112087000624
[24] DOI: 10.1017/S0022112005005148 · Zbl 1138.76304 · doi:10.1017/S0022112005005148
[25] DOI: 10.1063/1.870250 · Zbl 1149.76503 · doi:10.1063/1.870250
[26] DOI: 10.1017/S0022112077001700 · doi:10.1017/S0022112077001700
[27] DOI: 10.1063/1.1501545 · Zbl 1185.76262 · doi:10.1063/1.1501545
[28] DOI: 10.1006/jcph.1999.6382 · Zbl 0981.76075 · doi:10.1006/jcph.1999.6382
[29] DOI: 10.1017/S0022112075001966 · Zbl 0312.76051 · doi:10.1017/S0022112075001966
[30] Z. Flugwiss. 19 pp 319– (1971)
[31] DOI: 10.1098/rsta.1984.0024 · Zbl 0589.76071 · doi:10.1098/rsta.1984.0024
[32] DOI: 10.1098/rsta.1981.0001 · Zbl 0464.76045 · doi:10.1098/rsta.1981.0001
[33] Proc. R. Soc. Lond. A pp 564– (1952)
[34] DOI: 10.1121/1.1913245 · doi:10.1121/1.1913245
[35] DOI: 10.1017/S0022112083003195 · doi:10.1017/S0022112083003195
[36] DOI: 10.1016/0022-460X(72)90451-8 · doi:10.1016/0022-460X(72)90451-8
[37] DOI: 10.1017/S0022112078002670 · doi:10.1017/S0022112078002670
[38] DOI: 10.1016/j.jsv.2013.02.040 · doi:10.1016/j.jsv.2013.02.040
[39] DOI: 10.1063/1.3665141 · Zbl 06423297 · doi:10.1063/1.3665141
[40] DOI: 10.1007/s00348-008-0587-0 · doi:10.1007/s00348-008-0587-0
[41] DOI: 10.1017/jfm.2012.378 · Zbl 1275.76185 · doi:10.1017/jfm.2012.378
[42] DOI: 10.1017/S0022112005006397 · Zbl 1085.76519 · doi:10.1017/S0022112005006397
[43] DOI: 10.1016/0022-460X(80)90416-2 · doi:10.1016/0022-460X(80)90416-2
[44] J. Fluid Mech. 611 pp 175– (2008)
[45] DOI: 10.2514/3.61076 · doi:10.2514/3.61076
[46] J. Fluid Mech. 612 pp 107– (2008)
[47] DOI: 10.1017/S0022112004000163 · Zbl 1067.76507 · doi:10.1017/S0022112004000163
[48] DOI: 10.1016/0021-9991(87)90041-6 · Zbl 0619.76089 · doi:10.1016/0021-9991(87)90041-6
[49] DOI: 10.1016/j.jsv.2011.04.007 · doi:10.1016/j.jsv.2011.04.007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.