Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
In 1941, the Russian mathematician Andrei N. Kolmogorov deduced scaling laws for the velocity statistics of turbulent ows. At the core of the Kolmogorov theory lies the hypothesis that the scales in fully developed turbulence are statistically self-similar. It is now believed that the turbulent scales are not self-similar but intermittent and the scaling exponents of moments of velocity increments are anomalous, that is, the departures from Kolmogorov's self-similar scaling increase nonlinearly with the increasing order of the moment. Since high-order moments sample the tails of a probability distribution function, it is also believed that the intermittency in turbulence is associated with rare events. We have shown, using a compilation of data from experiments and direct numerical simulations, that intermittency is not merely associated with the rare events in the flow but is in fact present in the high frequency events. Thus our results motivate the theoretical study of anomalous scaling in the limit of zeroth order moments, unbiased by so-called rare events.
