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International Journal of Fluid Mechanics Research

ISSN Print: 1064-2277
ISSN Online: 2152-5102

International Journal of Fluid Mechanics Research


pages 539-567

Chaotic Small-Scale Velocity Fields as Prospective Models for Unresolved Turbulence in an Additive Decomposition of the Navier-Stokes Equations

E. C. Hylin
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506-0108, USA
James M. McDonough
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506-0046, USA

ABSTRACT

A novel approach to turbulence modeling, based on unaveraged governing equations and direct modeling of small-scale fluctuating quantities via discrete nonlinear dynamical systems (chaotic algebraic maps), is presented and compared (structurally) with widely-used turbulence modeling and simulation methods. It is shown that this new approach, termed additive turbulent decomposition (ATD), is similar to large-eddy simulation in some respects, but yet is distinctly different in that ATD employs filtering of computed solutions (a straightforward signal-processing problem) rather than complicated filtering of governing equations. This obviates the need to model Reynolds stresses (they no longer occur in the equations); instead, subgrid-scale primitive variables, e.g., fluctuating velocity components, can be modeled directly, thus providing a much closer link to physical laboratory experiments. The requirements that must be imposed to construct such models are thoroughly discussed, and a specific realization of this modeling approach is derived in detail.