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Nonlinear dynamical analysis of turbulence in a stable cloud layer.

A. J. Palmer1

  • 1NOAA Environmental Technology Laboratory, Boulder, Colorado 80303.

Chaos (Woodbury, N.Y.)
|March 1, 1995
PubMed
Summary

This study models turbulence in clouds using spectral methods, finding that cloud reflectivity data shows weaker coupling than Doppler data. The model

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Area of Science:

  • Atmospheric Physics
  • Fluid Dynamics
  • Turbulence Modeling

Background:

  • Turbulence in stable cloud layers is complex and difficult to model.
  • Understanding cloud turbulence dynamics is crucial for weather and climate science.
  • Previous studies have used radar data to infer turbulence characteristics.

Purpose of the Study:

  • To compute the Lyapunov dimension of the dynamical attractor for turbulence in a stable cloud layer.
  • To compare model results with experimental data from marine stratus clouds.
  • To investigate the influence of the turbulent Prandtl number on attractor dimension.

Main Methods:

  • An eight-mode truncated spectral model based on Burgers' approximation to the one-dimensional Navier-Stokes equations.
  • Computation of the Lyapunov dimension of the dynamical attractor.
  • Comparison with correlation dimension derived from radar Doppler and reflectivity time series.

Main Results:

  • The spectral model's results align with experimental data, supporting weak coupling for reflectivity time series.
  • The turbulent Prandtl number was identified as a parameter that can increase the model's attractor dimension.
  • The model's computed attractor dimension remained lower than the radar Doppler correlation dimension.

Conclusions:

  • The study provides insights into the dimensionality of cloud turbulence attractors.
  • Weak coupling is a plausible explanation for differences in correlation dimensions between reflectivity and Doppler data.
  • Further analysis suggests that even a non-truncated model would yield a lower attractor dimension than observed in radar Doppler data.

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