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SUMMARY:On describing mean flow dynamics in wall turbulence - Klewicki\, J
  (New Hampshire)
DTSTART:20080911T155000Z
DTEND:20080911T161000Z
UID:TALK13384@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The study of wall-flow dynamics and their scaling behaviors wi
 th increasing Reynolds number warrants considerable attention. Attempts to
  date\, however\, have primarily focused on questions relating to what sca
 ling behaviors occur\, rather than the dynamical reasons why they occur. G
 iven these considerations\, the present talk is organized in three parts. 
 In the first part it is shown that the predominant methodology for discern
 ing the dominant mechanisms associated with the mean flow dynamics is prob
 lematic\, and can lead to erroneous conclusions. In the second part we exa
 mine the Millikan-Izakson (inner/outer/overlap) arguments that underpin th
 e widely accepted derivation for a logarithmic mean profile. Existing rigo
 rous results from the theory of functions are outlined. They reveal that t
 he Millikan-Izakson arguments constitute something very close to a tautolo
 gy and embody little physics specific to turbulent wall-flows. The first t
 wo parts establish the context for the third. The presentation concludes w
 ith a physical interpretation of the mathematical conditions necessary for
  a logarithmic (or nearly logarithmic) mean profile. The basis for this in
 terpretation is the analysis of Fife et al.\, (2005 JFM 532}\, 165) which 
 reveals that the mean differential statement of Newtons second law rigorou
 sly admits a hierarchy of physical layers each having their own characteri
 stic length. These analyses show that the condition for exact logarithmic 
 dependence exists when the normalized equations of motion (normalized usin
 g the local characteristic length) attain a self-similar structure\, and p
 hysically indicate that the leading coefficient in the logarithmic law (vo
 n Karman constant) will only be truly constant when an exact self-similar 
 structure in the gradient of the turbulent force is attained across a rang
 e of layers of the hierarchy. These results are discussed relative to the 
 physics of boundary layer Reynolds number dependence and recent data indic
 ating that the von Karman constant varies for vary ing mean momentum balan
 ce.
LOCATION:Seminar Room 1\, Newton Institute
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