FLUCTUATING HYDRODYNAMICS AND PRINCIPAL OSCILLATION PATTERN-ANALYSIS

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x(i)(t) produced by systems whose dynamics are described by a linear Markov process x = Bx + xi. The matrix B gives the deterministic feedback and xi is a white noise vector with covariances <xi-i(t) xi-j(t')> = Q(ij)delta (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-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Benard convection.