MULTIFRACTAL SCALING FROM NONLINEAR TURBULENCE DYNAMICS - ANALYTICAL METHODS

We consider a general class of stochastic models of a turbulent cascade. They are based solely on the classical conceptions of local interactions and energy conservation. We show that such a model must necessarily exhibit strongly non-Gaussian fluctuations on small scales. This intermittent behavior is characterized by multifractal scaling. We develop analytical methods to calculate the anomalous scaling exponents without adjustable parameters and give numerical values for a specific model studied previously.