Garcia, A., and C. Penland, 1991: Fluctuating hydrodynamics and principal oscillation pattern analysis. J. Stat. Phys., 64, 1121-1132.
Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series xi(t) produced by systems whose dynamics are described by a linear Markov process dx/dt = Bx + ξ. The matrix B gives the deterministic feedback and ξ is a white noise vector with covariances <ξi(t) ξj(t')> = Qij δ(t-t'). The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Benard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrix B) and the stochastic fluxes (in the matrix Q) as given by Landau-Lifshitz fluxtuating hydrodynamics. Using this method, we find the Landau-Lifshitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Benard convection.