Nonlinear stability of the rotating Benard problem, the case Pr=1

Nonlinear conditional stability of the Benard problem with rotation and free boundaries is studied in this paper in the case of Prandtl number Pr = 1 by means of a generalized energy functional. Previously used functionals to study this problem fail in the case Pr = 1. A new functional is proposed and coincidence of linear and nonlinear stability boundary is proved for moderate Taylor numbers T. The coincidence ends at the same value T = 80 pi(4) as in the case Pr > 1. The marginal Rayleigh number of nonlinear conditional stability grows asymptotically with the square root of the Taylor number as opposed to the critical Rayleigh number of linearized stability which grows with the 2/3 power of T.