Abstract: By using the priori estimates, Lipschitz continuity and squeezing estimates of the high frequency of the solutions, we studied the problems of stability and finiteness of fractal dimension of solutions to the  stochastic convection Brinkman-Forchheimer (CBF) equations driven by colored noise, and obtained the existence of random exponential attractors for these equations.

Key words: colored noise, fractal dimension, convection Brinkman-Forchheimer equation, random exponential attractor