EDDY VISCOSITY OF 3-DIMENSIONAL FLOW

• Type: Article in International Scientific Journal
• Date: 1995

Authors

WIRTH, A (Author) Other; GAMA, S (Author) FEUP; FRISCH, U (Author) Other

Journal

Title: Journal of Fluid Mechanics

Vol. 288

Pages: 249-264

ISSN: 0022-1120

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 24 Citations

Scopus - 23 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

Other information

Authenticus ID: P-001-H1D

DOI: 10.1017/s0022112095001133

Abstract (EN): Detailed theoretical and numerical results are presented for the eddy viscosity of three-dimensional forced spatially periodic incompressible flow. As shown by Dubrulle & Frisch (1991), the eddy viscosity, which is in general a fourth-order anisotropic tenser, is expressible in terms of the solution of auxiliary problems. These are, essentially, three-dimensional linearized Navier-Stokes equations which must be solved numerically. The dynamics of weak large-scale perturbations of wavevector k is determined by the eigenvalues - called here 'eddy viscosities' - of a two by two matrix, obtained by contracting the eddy viscosity tenser with two k-vectors and projecting onto the plane transverse to k to ensure incompressibility. As a consequence, eddy viscosities in three dimensions, but not in two, can become complex. It is shown that this is ruled out for flow with cubic symmetry, the eddy viscosities of which may, however, become negative. An instance is the equilateral ABC-flow (A = B = C = 1). When the wavevector k is in any of the three coordinate planes, at least one of the eddy Viscosities becomes negative for R = 1/nu > R(c) similar or equal to 1.92. This leads to a large-scale instability occurring for a value of the Reynolds number about seven times smaller than instabilities having the same spatial periodicity as the basic flow.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16