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On the k1 -1 scaling in sink-flow turbulent boundary layers

Dixit, SA and Ramesh, ON (2013) On the k1 -1 scaling in sink-flow turbulent boundary layers. Journal of Fluid Mechanics, 737. pp. 329-348.

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Scaling of the streamwise velocity spectrum Φ11 (k1) in the so-called sink-flow turbulent boundary layer is investigated in this work. The present experiments show strong evidence for the k1 -1 scaling i.e. Φ11 (k1)= A1Uτ 2k1 -1, where k1 is the streamwise wavenumber and Uτ is the friction velocity. Interestingly, this k1 -1 scaling is observed much farther from the wall and at much lower flow Reynolds number (both differing by almost an order of magnitude) than what the expectations from experiments on a zero-pressure-gradient turbulent boundary layer flow would suggest. Furthermore, the coefficient A1 in the present sink-flow data is seen to be non-universal, i.e. A1 varies with height from the wall; the scaling exponent -1 remains universal. Logarithmic variation of the so-called longitudinal structure function, which is the physical-space counterpart of spectral k1 -1 scaling, is also seen to be non-universal, consistent with the non-universality of A1. These observations are to be contrasted with the universal value of A1 (along with the universal scaling exponent of -1) reported in the literature on zero-pressure-gradient turbulent boundary layers. Theoretical arguments based on dimensional analysis indicate that the presence of a streamwise pressure gradient in sink-flow turbulent boundary layers makes the coefficient A1 non-universal while leaving the scaling exponent -1 unaffected. This effect of the pressure gradient on the streamwise spectra, as discussed in the present study (experiments as well as theory), is consistent with other recent studies in the literature that are focused on the structural aspects of turbulent boundary layer flows in pressure gradients (Harun et al., J. Fluid Mech., vol. 715, 2013, pp. 477-498); the present paper establishes the link between these two. The variability of A1 accommodated in the present framework serves to clarify the ideas of universality of the k1 -1 scaling.

Item Type: Article
Additional Information: Copyright of this article belongs to Cambridge University Press
Uncontrolled Keywords: Atmospheric thermodynamics; Boundary layers; Pressure gradient; Reynolds number; Scaling laws; Turbulence; Turbulent flow, Boundary layer structure; Dimensional analysis; Stream-wise velocities; Theoretical arguments; Turbulent boundary layer flow; Turbulent boundary layers; Universal scaling exponents; Zero-pressure gradient turbulent boundary layer, Boundary layer flow, flow structure; flow velocity; pressure gradient; Reynolds number; turbulent boundary layer
Subjects: Meteorology and Climatology
Depositing User: IITM Library
Date Deposited: 12 Nov 2015 09:06
Last Modified: 12 Nov 2015 09:06

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