Exponentially growing solutions in homogeneous Rayleigh-Benard convection

Details Exponentially growing solutions in homogeneous Rayleigh-Benard convection Exponentially growing solutions in homogeneous Rayleigh-Benard convection

2006-02-18

arxiv.org/abs/nlin/0602040v1

Phys. Rev. E 73, 035301(R) (2006)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, to be published in Phys. Rev. E - rapid communications

Scientific paper

10.1103/PhysRevE.73.035301

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard 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 non-linear 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.

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