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Coherent structures, uniform momentum zones and the streamwise energy spectrum in wall-bounded turbulent flows. (English) Zbl 1430.76279
Summary: Large-scale motions (LSMs) in wall-bounded turbulent flows have well-characterised instantaneous structural features [L. S. G. Kovasznay et al., “Large-scale motion in the intermittent region of a turbulent boundary layer”, ibid. 41, No. 2, 283-325 (1970; doi:10.1017/S0022112070000629); C. D. Meinhart and R. J. Adrian, “On the existence of uniform momentum zones in a turbulent boundary layer”, Phys. Fluids 7, No. 4, 694-669 (1998; doi:10.1063/1.868594)] and a known spectral signature [J. P. Monty et al., J. Fluid Mech. 632, 431-442 (2009; Zbl 1183.76036)]. This work aims to connect these previous observations through the development and analysis of a representative model for LSMs. The model is constructed to be consistent with the streamwise energy spectrum [loc. cit.] and amplification characteristics of the Navier-Stokes equations [the second author and A. S. Sharma, ibid. 658, 336-382 (2010; Zbl 1205.76138)], and is found to naturally recreate characteristics of instantaneous turbulent structures, including a bulge shape [Kovasznay et al., loc. cit.] and the presence of uniform momentum zones [Meinhart and Adrian, loc. cit.] in the streamwise velocity field. The observed structural similarity between the LSM representative model and instantaneous experimental data supports the use of travelling wave models to connect statistical and instantaneous descriptions of coherent structures, and clarifies a simple general equivalency between symmetry in a Reynolds-decomposed velocity field and asymmetry in the laboratory frame.

MSC:
76F40 Turbulent boundary layers
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