It is shown that homogeneous Rayleigh-Bénard flow, i.e., Rayleigh-Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full nonlinear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.
Physical Review E
- Pub Date:
- March 2006
- Turbulent transport processes;
- Nonlinear Sciences - Chaotic Dynamics
- 4 pages, 3 figures, to be published in Phys. Rev. E - rapid communications