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Eighth International Symposium on Turbulence and Shear Flow Phenomena
August, 28-30, 2013, Poitiers, Futuroscope, France

DOI: 10.1615/TSFP8

ON GEOMETRICALLY SELF-SIMILAR MODES IN WALL-BOUNDED TURBULENT FLOWS

pages 1-6
DOI: 10.1615/TSFP8.1280
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ABSTRACT

A gain-based low-rank approximation (McKeon & Sharma, 2010) of the Navier-Stokes equations is utilized to describe the possibility of geometrically self-similar modes in the overlap region of wall-bounded turbulent flows. We establish that a necessary condition for existence of self-similar velocity fluctuations is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes. It is shown that the elements of a hierarchy are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity: The height and width of the modes scale linearly and the length of the modes scales quadratically with the critical wall-normal location.

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