Mathematical models with exact renormalization for turbulent transport. II: Fractal interfaces, non-Gaussian statistics and the sweeping effect
[For part I see: Commun. Math. Phys. 131, No. 2, 381-429 (1990; Zbl 0703.76042).] This paper continues the study of a model for turbulent transport with an exact renormalization theory which has recently been proposed and developed by the authors. Three important topics are analyzed with complete mathematical rigor for this model: (1) Renormalized higher order statistics of a passively advected scalar such as the pair distance distribution and the fractal dimension of interfaces, (2) the effect of non-Gaussian turbulent velocity statistics on renormalization theory, (3) the ``sweeping'' effect of additional large scale mean velocities. A special emphasis is placed on renormalization theory in the vicinity of the value of the analogue of the Kolmogorov-spectrum in the model.
scientific article; zbMATH DE number 61999
scientific article