Eddy viscosity of parity-invariant flow

Details Eddy viscosity of parity-invariant flow Eddy viscosity of parity-invariant flow

May 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrva..43.5355d&link_type=abstract

Physical Review A (ISSN 1050-2947), vol. 43, May 15, 1991, p. 5355-5364.

Statistics

Computation

57

Computational Fluid Dynamics, Eddy Viscosity, Incompressible Flow, Molecular Flow, Transport Theory, Turbulence Models, Kolmogoroff Theory, Low Reynolds Number, Parallel Flow, Perturbation Theory, Stream Functions (Fluids), Tensor Analysis

Scientific paper

A general formalism is developed to determine eddy viscosities for incompressible flow of arbitrary dimensionality subject to forcing periodic in space and time. The dynamics of weak large-scale perturbations is obtained by a multiscale analysis. The large-scale behavior is found to be formally diffusive whenever the basic flow is parity invariant, that is, possesses a center of symmetry. The eddy viscosity is in general a fourth-order tensor, for which a compact representation is provided. Explicit expressions of the eddy-viscosity tensor are given: (1) for basic flow with low Reynolds numbers; and (2) when the basic flow is layered, i.e., depends only on one space coordinate and time. For flows presenting less symmetry than the Kolmogorov flow, the first large-scale instability is usually found not to be transverse, thus breaking the spatial periodicity of the basic flow.

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