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

Rashad Moarref
Graduate Aerospace Laboratories California Institute of Technology Pasadena, CA 91125, USA

Ati S. Sharma
Department of Aeronautics Imperial College London, SW7 2AZ UK; Engineering and the Environment University of Southampton Highfield, Southampton, SO17 1BJ, UK

Joel A. Tropp
Computing & Mathematical Sciences California Institute of Technology Pasadena, CA 91125, USA

Beverley J. McKeon
Department of Aeronautics, Imperial College London, SW7 2AZ, UK; Graduate Aerospace Laboratories California Institute of Technology Pasadena, CA 91125, USA

Sinopsis

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.