Two models of truncated Navier--Stokes equations on a two-dimensional torus

Journal Article · Tue Feb 01 00:00:00 EST 1983 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.864156· OSTI ID:6516493

Franceschini, V

Two truncations of the Navier--Stokes equations for an incompressible fluid on a two-dimensional torus are numerically investigated. The two models, an eight-mode truncation and a nine-mode extension of it, exhibit almost completely different behaviors. Only two aspects appear to be common to both. First, in contrast to all the previously studied models, turbulence takes place at low Reynolds numbers and for critical values close to each other. Second, there is a parameter interval for which the same stable periodic orbit is present in both models. The main feature of the two truncations is a very rich phenomenology, with many different bifurcations of closed orbits. Turbulence is reached through a sequence of period-doubling bifurcations in the eight-mode model, and via a tangent bifurcation in the nine-mode one. Sequences of infinite bifurcations, the presence in a very narrow range of a stable closed orbit with a quite long period, a homoclinic bifurcation, and the coexistence of strange attractors with attracting periodic orbits, appear to be the more interesting phenomena.

• Research Organization: Los Alamos National Laboratory, Center for Nonlinear Studies, MS 258, Los Alamos, New Mexico 87545
• OSTI ID: 6516493
• Journal Information: Phys. Fluids; (United States), Vol. 26:2
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
INCOMPRESSIBLE FLOW
NAVIER-STOKES EQUATIONS
TURBULENCE
FLOW MODELS
NUMERICAL SOLUTION
REYNOLDS NUMBER
TORI
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
640410* - Fluid Physics- General Fluid Dynamics