# zbMATH — the first resource for mathematics

Investigation of three-dimensional structure of fine scales in a turbulent jet by using cinematographic stereoscopic particle image velocimetry. (English) Zbl 1151.76323
Summary: Cinematographic stereoscopic particle image velocimetry measurements were performed to resolve small and intermediate scales in the far field of an axisymmetric co-flowing jet. Measurements were performed in a plane normal to the axis of the jet and the time-resolved measurement was converted to quasi-instantaneous three-dimensional data by using Taylor’s hypothesis. The quasi-instantaneous three-dimensional data enabled computation of all nine components of the velocity gradient tensor over a volume. The results based on statistical analysis of the data, including computation of joint p.d.f.s and conditional p.d.f.s of the principal strain rates, vorticity and dissipation, are all in agreement with previous numerical and experimental studies, which validates the quality of the quasi-instantaneous data. Instantaneous iso-surfaces of the principal intermediate strain rate ($$\beta$$) show that sheet-forming strain fields (i.e. $$\beta > 0$$) are themselves organized in the form of sheets, whereas line-forming strain fields ($$\beta < 0$$) are organized into smaller spotty structures (not lines). Iso-surfaces of swirling strength (a vortex identification parameter) in the volume reveal that, in agreement with direct numerical simulation results, the intense vortex structures are in the form of elongated ‘worms’ with characteristic diameter of approximately $$10\eta$$ and characteristic length of $$60-100\eta$$. Iso-surfaces of intense dissipation show that the most dissipative structures are in the form of sheets and are associated with clusters of vortex tubes. Approximately half of the total dissipation occurs in structures that are generally sheet-like, whereas the other half occurs in broad indistinct structures. The largest length scale of dissipation sheets is of order $$60\eta$$ and the characteristic thickness (in a plane normal to the axis of the sheet) is about $$10\eta$$. The range of scales between $$10\eta$$ (thickness of dissipation sheets, diameter of vortex tubes) to $$60\eta$$ (size of dissipation sheet or length of vortex tubes) is consistent with the bounds for the dissipation range in the energy and dissipation spectrum as inferred from the three-dimensional model energy spectrum.

##### MSC:
 76-05 Experimental work for problems pertaining to fluid mechanics 76F55 Statistical turbulence modeling
Full Text:
##### References:
 [1] DOI: 10.1017/S0022112005004040 · Zbl 1070.76033 [2] DOI: 10.1103/PhysRevLett.64.415 [3] DOI: 10.1017/S0022112098008726 · Zbl 0955.76508 [4] DOI: 10.1088/0957-0233/12/11/320 [5] DOI: 10.1017/S0022112096000651 [6] DOI: 10.1016/0169-5983(91)90026-F [7] DOI: 10.1007/s003480070032 [8] DOI: 10.1017/S0022112056000317 · Zbl 0071.40603 [9] DOI: 10.1063/1.858333 [10] Batchelor, Proc. R. Soc. Lond. 199 pp 238– (1949) [11] Ruetsch, Phys. Fluids 3 pp 1587– (1991) [12] DOI: 10.1063/1.866513 [13] Raffel, Particle Image Velocimetry (1998) [14] DOI: 10.1017/S0022112082001268 [15] DOI: 10.1017/S0022112005008207 · Zbl 1222.76053 [16] DOI: 10.1063/1.863055 [17] Pope, Turbulent Flows (2000) · Zbl 0966.76002 [18] DOI: 10.1017/S0022112091000526 · Zbl 0729.76599 [19] Mullin, Phys. Fluids 18 pp 1– (2006) [20] Mullin, Phys. Fluids 18 pp 1– (2006) [21] Monin, Statistical Fluid Mechanics (1975) [22] DOI: 10.1007/s00348-003-0603-3 [23] Melander, Phys. Rev. 48 pp 2669– (1993) [24] DOI: 10.1063/1.863957 · Zbl 0536.76034 [25] DOI: 10.1063/1.868440 · Zbl 0825.76359 [26] DOI: 10.1017/S0022112071002581 [27] DOI: 10.1017/S002211209900467X · Zbl 0946.76030 [28] DOI: 10.1017/S0022112062000518 · Zbl 0112.42003 [29] DOI: 10.1038/nature01334 [30] DOI: 10.1063/1.858252 · Zbl 0754.76050 [31] DOI: 10.1143/JPSJ.57.1532 [32] DOI: 10.1017/S0022112085001136 · Zbl 0587.76080 [33] DOI: 10.1017/S0022112094003319 · Zbl 0800.76157 [34] DOI: 10.1017/S0022112091001957 · Zbl 0721.76036 [35] DOI: 10.1017/S0022112093002393 · Zbl 0800.76156 [36] DOI: 10.1017/S0022112095000462 · Zbl 0847.76007 [37] DOI: 10.1017/S0022112091000368 · Zbl 0729.76594 [38] DOI: 10.1016/S0169-5983(97)00022-1 · Zbl 1051.76585 [39] DOI: 10.1007/s00348-007-0303-5 [40] DOI: 10.1017/S0022112092002325 [41] DOI: 10.1063/1.1691966 [42] Frisch, Turbulence: The Legacy of A. N. Kolmogorov (1995) · Zbl 0832.76001 [43] DOI: 10.1088/1468-5248/1/1/011 · Zbl 1082.76554 [44] Su, Phys. Fluids 8 pp 507– (1996) [45] DOI: 10.1103/PhysRevLett.67.983 [46] DOI: 10.1146/annurev.fluid.29.1.435 [47] DOI: 10.1016/S0997-7546(99)80026-0 · Zbl 0935.76010 [48] DOI: 10.1023/B:APPL.0000044408.46141.26 · Zbl 1081.76564 [49] DOI: 10.1017/S0022112005004726 · Zbl 1071.76015 [50] DOI: 10.1017/S002211208100181X · Zbl 0476.76051 [51] DOI: 10.1017/S0022112094001370
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.