Nonlinear dynamical analysis of turbulence in a stable cloud layer

An eight mode truncated spectral model based on Burgers' approximation to the one-dimensional Navier-Stokes equations is used to compute the Lyapunov dimension of the dynamical attractor for turbulence in a stable cloud layer. The model results are compared with the correlation dimension obtained earlier from a time series of radar Doppler and reflectivity signals from a turbulent layer in a marine stratus cloud. The analysis supports a weak coupling explanation for the lower correlation dimension found for the reflectivity time series compared with that for the Doppler time series. Turbulent Prandtl number emerges from the analysis as a flow parameter which can enlarge the dimension of the model's dynamical attractor, but the attractor dimension computed for the model remains lower than the radar Doppler correlation dimension. Linear stability analysis of the model's equilibrium states suggests that a nontruncated version of the model will possess an attractor which is also of lower dimension than the radar Doppler correlation dimension. (c) 1995 American Institute of Physics.