# zbMATH — the first resource for mathematics

Effects of initial conditions in decaying turbulence generated by passive grids. (English) Zbl 1118.76008
Summary: The effects of initial conditions on grid turbulence are investigated for low to moderate Reynolds numbers. Four grid geometries are used to yield variations in initial conditions, and a secondary contraction is introduced to improve the isotropy of the turbulence. The hot-wire measurements, believed to be the most detailed to date for this flow, indicate that initial conditions have a persistent impact on the large-scale organization of the flow over the length of the tunnel. The power-law coefficients, determined via an improved method, also depend on the initial conditions. For example, the power-law exponent $$m$$ is affected by the various levels of large-scale organization and anisotropy generated by different grids and the shape of the energy spectrum at low wavenumbers. However, the results show that these effects are primarily related to deviations between the turbulence produced in the wind tunnel and true decaying homogeneous isotropic turbulence. Indeed, when isotropy is improved and the intensity of the large-scale periodicity, which is primarily associated with round-rod grids, is decreased, the importance of initial conditions on both the character of the turbulence and $$m$$ is diminished. However, even in the case where the turbulence is nearly perfectly isotropic, $$m$$ is not equal to $$- 1$$, nor does it show an asymptotic trend in $$x$$ towards this value, as suggested by recent analysis. Furthermore, the evolution of the second- and third-order velocity structure functions satisfies equilibrium similarity only approximately.

##### MSC:
 76-05 Experimental work for problems pertaining to fluid mechanics 76F05 Isotropic turbulence; homogeneous turbulence
Full Text:
##### References:
 [1] DOI: 10.1017/S0022112096007562 · doi:10.1017/S0022112096007562 [2] DOI: 10.1017/S0022112092002180 · Zbl 0756.76030 · doi:10.1017/S0022112092002180 [3] Batchelor, Proc. R. Soc. Lond. 190 pp 534– (1947) [4] DOI: 10.1017/S0022112090002919 · doi:10.1017/S0022112090002919 [5] Batchelor, Q. Appl. Maths 6 pp 97– (1948) [6] Michelet, C. R. Acad. Sci. Paris II b 326 pp 621– (1998) [7] Batchelor, Proc. Camb. Phil. Soc. 43 pp 533– (1947) [8] DOI: 10.1063/1.868319 · Zbl 0825.76278 · doi:10.1063/1.868319 [9] DOI: 10.1017/S0022112003004713 · Zbl 1073.76044 · doi:10.1017/S0022112003004713 [10] DOI: 10.1063/1.1694093 · doi:10.1063/1.1694093 [11] DOI: 10.1017/S0022112098002547 · Zbl 0941.76516 · doi:10.1017/S0022112098002547 [12] Antonia, J. Fluid Mech. 332 pp 395– (1997) [13] DOI: 10.1007/s00348-005-0022-8 · doi:10.1007/s00348-005-0022-8 [14] DOI: 10.1017/S0022112004008456 · Zbl 1069.76024 · doi:10.1017/S0022112004008456 [15] Korneyev, Fluid Mech. Sov. Res. 5 pp , 37– (1976) [16] Kolmogorov, C. R. Acad. Sci. URSS 30 pp 301– (1941) [17] DOI: 10.1017/S0022112066001071 · doi:10.1017/S0022112066001071 [18] von K?rm?n, Proc. R. Soc. Lond. 164 pp 192– (1938) [19] DOI: 10.1017/S0022112002003579 · Zbl 1063.76507 · doi:10.1017/S0022112002003579 [20] DOI: 10.1063/1.868366 · Zbl 0832.76031 · doi:10.1063/1.868366 [21] George, AIAA J. 42 pp 438– (2004) [22] George, Phys. Fluids 4 pp 1492– (1992) · Zbl 0754.76042 · doi:10.1063/1.858423 [23] DOI: 10.1017/S0022112074000607 · doi:10.1017/S0022112074000607 [24] DOI: 10.1016/0735-1933(83)90032-5 · doi:10.1016/0735-1933(83)90032-5 [25] Dryden, Q. Appl. Maths 1 pp 7– (1943) [26] DOI: 10.1063/1.1476300 · Zbl 1185.76103 · doi:10.1063/1.1476300 [27] DOI: 10.1088/0957-0233/7/10/006 · doi:10.1088/0957-0233/7/10/006 [28] DOI: 10.1017/S0022112095000929 · doi:10.1017/S0022112095000929 [29] DOI: 10.1017/S0022112066000338 · doi:10.1017/S0022112066000338 [30] Zhou, Exps. Fluids 34 pp 449– (2003) · doi:10.1007/s00348-002-0566-9 [31] DOI: 10.1063/1.868337 · Zbl 0827.76027 · doi:10.1063/1.868337 [32] Burattini, Phys. Rev. 73 pp 066304– (2006) [33] DOI: 10.1063/1.1762265 · doi:10.1063/1.1762265 [34] DOI: 10.1007/s00348-004-0889-9 · doi:10.1007/s00348-004-0889-9 [35] DOI: 10.1017/S0022112066000806 · doi:10.1017/S0022112066000806 [36] DOI: 10.1063/1.869733 · doi:10.1063/1.869733 [37] Uberoi, J. Aero. Sci. 23 pp 754– (1956) · doi:10.2514/8.3651 [38] DOI: 10.1063/1.862168 · doi:10.1063/1.862168 [39] DOI: 10.1007/s003480050030 · doi:10.1007/s003480050030 [40] DOI: 10.1017/S0022112092002325 · doi:10.1017/S0022112092002325 [41] Batchelor, Proc. R. Soc. Lond. 193 pp 539– (1948)
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.