Abstract
The dynamics of the Lorenz model in the “turbulent” regime (r>r T is investigated by applying methods for treating many-body systems. Symmetry properties are used to derive relations between correlation functions. The basic ones are evaluated numerically and discussed for several values of the parameterr. A theory for the spectra of the two independent relaxation functions is presented using a dispersion relation representation in terms of relaxation kernels and characteristic frequencies. Their role in the dynamics of the system is discussed and it is shown that their numerical values increase in proportion to √r. The approximation of the relaxation kernels that represent nonlinear coupling between the variables by a relaxation time expression and a simple mode coupling approximation, respectively, is shown to explain the two different fluctuation spectra. The coupling strength for the modes is determined by a Kubo relation imposing selfconsistency. Comparison with the “experimental” spectra is made for three values ofr.
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Lücke, M. Statistical dynamics of the Lorenz model. J Stat Phys 15, 455–475 (1976). https://doi.org/10.1007/BF01020800
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DOI: https://doi.org/10.1007/BF01020800