# American Institute of Mathematical Sciences

August  2009, 24(3): 781-807. doi: 10.3934/dcds.2009.24.781

## Time averaging in turbulence settings may reveal an infinite hierarchy of length scales

 1 Department of Mathematics, University of Utah, 155 S. 1400 E., Salt Lake City, UT 84112-0090, United States 2 Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, United States 3 Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802, United States

Received  December 2007 Revised  November 2008 Published  April 2009

The problem of discerning key features of steady turbulent flow adjacent to a wall has drawn the attention of some of the most noted fluid dynamicists of all time. Standard examples of such features are found in the mean velocity profiles of turbulent flow in channels, pipes or boundary layers. The aim of this article is to explain and further develop the recent concept of scaling patch for the time-averaged equations of motion of incompressible flow made highly turbulent by friction at a fixed boundary (introduced in recent papers by Wei et al, Fife et al, and Klewicki et al.) Besides outlining ways to identify the patches, which provide the scaling structure of mean profiles, a critical comparison will be made between that approach and more traditional ones.
Our emphasis will be on the question of how and how well these arguments supply insight into the structure of the mean flow profiles. Although empirical results may initiate the search for explanations, they will be viewed simply as means to that end.
Citation: Paul Fife, Joseph Klewicki, Tie Wei. Time averaging in turbulence settings may reveal an infinite hierarchy of length scales. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 781-807. doi: 10.3934/dcds.2009.24.781
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