Bifurcations in a three-mode model of the Navier-Stokes equation

A. COSTA, D. GOMEZ, AND S. PONCE DAWSON

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 1988 vol. 38 p. 2037 - 2043

1050-2947

We analytically follow the nonlinear evolution of three coupled modes of the two-dimensional Navier-Stokes equation in an externally driven and dissipative case. As the external force amplitude (control parameter) is increased, a node-to-node bifurcation appears, giving rise to new stable equilibria.We find that the most relevant set of three modes contributes to the energy and enstrophy cascades in the same directions as in fully developed turbulence. We model the coupling with the remaining modes as a white-noise contribution, deriving the equilibrium distribution function forthe corresponding Fokker-Planck equation.