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Fluctuating hydrodynamics and principal oscillation pattern analysis

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Abstract

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 x=Bx + ξ. The matrixB gives the deterministic feedback and ξ is a white noise vector with covariances 〈ξ(t)ξ j (t′〉*Q ij 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-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) 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-Bénard convection.

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Authors and Affiliations

  1. Department of Physics, San Jose State University, 95192-0106, San Jose, California

    Alejandro García

  2. Cooperative Institute for Research in the Environmental Sciences, University of Colorado, 80309-2016, Boulder, Colorado

    Cécile Penland

Authors
  1. Alejandro García
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  2. Cécile Penland
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García, A., Penland, C. Fluctuating hydrodynamics and principal oscillation pattern analysis. J Stat Phys 64, 1121–1132 (1991). https://doi.org/10.1007/BF01048818

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