NEGATIVE EDDY VISCOSITY IN ISOTROPICALLY FORCED 2-DIMENSIONAL FLOW - LINEAR AND NONLINEAR DYNAMICS

• Type: Article in International Scientific Journal
• Date: 1994

Authors

GAMA, S (Author) FEUP; VERGASSOLA, M (Author) Other; FRISCH, U (Author) Other

Journal

Title: Journal of Fluid Mechanics

Vol. 260

Pages: 95-126

ISSN: 0022-1120

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 79 Citations

Scopus - 79 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

Other information

Authenticus ID: P-001-KD7

DOI: 10.1017/s0022112094003459

Abstract (EN): The existence of two-dimensional flows with an isotropic and negative eddy viscosity is demonstrated. Such flows, when subject to a very weak large-scale perturbation of wavenumber k will amplify it with a rate proportional to k2, independent of the direction. Specifically, it is assumed that the basic (unperturbed) flow is space-time periodic, possesses a centre of symmetry (parity-invariance) and has three- or six-fold rotational invariance to ensure isotropy of the eddy-viscosity tensor. The eddy viscosities emerging from the multiscale analysis are calculated by two different methods. First, there is an expansion in powers of the Reynolds number which can be carried out to large orders, and then extended analytically (thanks to a meromorphy property) beyond the disk of convergence. Secondly, there is a spectral method. The two methods typically agree within a fraction of 1%. A simple example, the 'decorated hexagonal flow', of a time-independent flow with isotropic negative eddy viscosity is given. Flows with randomly chosen Fourier components and the required symmetry have typically a 30% chance of developing a negative eddy viscosity when the Reynolds number is increased. For basic flow driven by a prescribed external force and sufficiently strong large-scale flow, the analysis is extended to the nonlinear regime. It is found that the large-scale dynamics is governed by a Navier-Stokes or a Navier-Stokes-Kuramoto-Sivashinsky equation, depending on the sign and strength of the eddy viscosity. When the driving force is not mirror-symmetric, a new 'chiral' nonlinearity appears. In special cases, the large-scale equation reduces to the Burgers equation. With chiral forcing, circular vortex patches are strongly enhanced or attenuated, depending on their cyclonicity.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 32