A33B-0149
Law-of-the-wall buffer layer explained by a simplified cospectral budget model
Wednesday, 16 December 2015
Poster Hall (Moscone South)
Kaighin A Mccoll, Massachusetts Institute of Technology, Civil and Environmental Engineering, Cambridge, MA, United States, Gabriel George Katul, Duke University, Durham, NC, United States, Pierre Gentine, Columbia University of New York, Palisades, NY, United States and Dara Entekhabi, Massachusetts Institute of Technology, CEE, Cambridge, MA, United States
Abstract:
A series of recent studies have shown that a model of the turbulent vertical velocity variance spectrum (Fvv) combined with a simplified cospectral budget can reproduce many macroscopic flow properties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the “law of the wall”. While the theory reasonably models the MVP’s logarithmic layer, the modelled buffer layer displays insufficient curvature compared to measurements at moderate Reynolds number. The theory is re-examined here using a DNS dataset at moderate Reynolds number. Starting with several hypotheses for the cause of the ‘missing’ curvature, it is shown that it is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed Fvv and the idealized form used in the previous model. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for the presence of a wall, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported Fvv rather than the idealized form previously used reproduces the missing buffer layer curvature to high fidelity thereby confirming the “spectral link” between Fvv and the MVP. A major departure between the idealized Fvv previously employed and those reported from DNS is the invariance with distance from the wall of the cross-over scale to the inertial subrange in Fvv. This invariance is presumably due to the presence of streaks within the buffer region whose dimensions do not scale with distance from the wall. Comparisons between DNS reported and modeled cospectra are also discussed. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., Fvv) representing the microstates of the flow.
