We use the theory of stochastic differential equations with rapidly fluctuating coefficients to study the statistical dynamics of the Lorenz model in the turbulent region. On the assumption that the system is ergodic we are able to calculate self-consistently several basic statistical quantities in terms of the parameters of the model. Our results are in good agreement with numerical computations.
Key words Turbulence - Rayleigh-Bénard layer - random behavior of nonlinear differential equations - fluctuation spectra - stochastic differential equations