Turbulent mixing: the roots of intermittency

Mixing in fully developed incompressible turbulent flows is known to lead to a cascade of discontinuity fronts of passive scalar fields; these fronts make the tracer fields strongly intermittent and give rise to an anomalous scaling of structure functions. Here, a simple model, essentially a one-dimensional (1D) variant of Baker's map, is developed, which captures the main mechanism responsible for the emergence of the discontinuities. The model is studied both numerically and analytically. In particular, the structure function scaling exponent zeta(p) is derived; for the Kolmogorov turbulence, zeta(p) = 2/3 log(3) (p + 1). The analytical findings are consistent with simulations, and explain the results of a series of numerical and experimental studies.