Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-07-28
Nonlinear Sciences
Chaotic Dynamics
35 pages, 28 figures, references are changed, mirror changes in the text
Scientific paper
Model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using the field theoretic renormalization group and the operator product expansion. The inertial-range stability of the corresponding scaling regime is established. The anomalous scaling of the single-time structure functions is studied and the corresponding anomalous exponents are calculated. Their dependence on the compressibility parameter and anisotropy parameters is analyzed. It is shown that, as in the isotropic case, the presence of compressibility leads to the decreasing of the critical dimensions of the important composite operators, i.e., the anomalous scaling is more pronounced in the compressible systems. All calculations are done to the first order in $\epsilon$.
Jurcisin Marian
Jurcisinova E.
Remecky R.
Scholtz Martin
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