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Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. (English) Zbl 1181.76008
Summary: We investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer [N. Hutchins and I. Marusic [Phil. Trans. R. Soc. Lond. A 365, 647–664 (2007; Zbl 1152.76421)] have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations [A. A. Townsend, The Structure of Turbulent Shear Flow, 2nd ed., (Cambridge University Press) (1976; Zbl 0435.76033)], we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at \(Re_{\tau } \sim 10^{3}-10^{4}\) to atmospheric surface layer measurements at \(Re_{\tau } ~ 10^{6}\).

MSC:
76-05 Experimental work for problems pertaining to fluid mechanics
76F40 Turbulent boundary layers
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