Statistical Structure at the Wall of the High Reynolds Number Turbulent Boundary Layer |
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Authors: | JCR Hunt P Carlotti |
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Institution: | (1) Departments of Space Climate Physics and Geological Sciences, University College, London WC1, U.K.; and J.M. Burgers Centre, Delft University of Technology, Delft, The Netherlands;(2) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K.; and Centre National de Recherches Météorologiques, Météo France, Toulouse, France |
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Abstract: | The one and two-point statistical structure of very high Reynolds number turbulence in the surface layer near a rigid `wall'
is analysed. The essential mechanisms for turbulent eddies impinging on the wall are studied using linearised rapid distortion
theory, which show how the mean shear and blocking actions of the surface act first independently and then, over the life
time of the eddy, interactively. Previous analytical results are reinterpreted and some new results are derived to show how
the integral length scales, cross correlations and spectra of the different components of the turbulence are distorted depending
on the form of the spectra of eddies above the surface layer and how they are related to motions of characteristic eddy structures
near the surface. These results are applied to derive some quantitative and qualitative predictions in the surface layers
(SL), where the eddies are affected by local shear dynamics, and in the `eddy surface layer' (ESL) where quasi independents
loping elongated eddies interact directly with the wall, and where there is a large range of wave number within which the
spectra of the horizontal velocity components are proportional to k
−1. The longest eddies in the boundary layer occur near the wall. Field experiments agree with the theoretical model predictions
for the quite different forms for the spectra, cospectra and cross correlations for the vertical and horizontal components
of the velocity field. By showing that in SL the energy exchange between the large and small scale eddies is local(`staircase')
energy cascade, whereas in ESL there is a direct nonlocal (`elevator-like')energy transfer to the small scales, it is shown
why the thickness of the ESL increases over rougher surfaces and as the Reynolds number decreases.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | energy transfer RDT spectra surface layer |
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