The multifractal spectrum of the dissipation field in turbulent flows

It has been pointed out (Mandelbrot 1974) that the turbulent energy dissipation field has to be regarded as a non-homogenous fractal and that other more general quantities than the fractal dimension of its support have to be invoked for describing its scaling (metric) properties completely. This work is an attempt on amplifying this idea by using direct experimental data, and on making proper connections between the multifractal approach (described in section 2) and the traditional language used in the turbulence literature. In the multifractal approach (Frisch & Parisi, 1983), the local behavior of the dissipation rate is described by a fractal power-law. We verify that this is so, and use it to measure the (infinite) set of 'generalized dimensions', and thus obtain the multifractal spectrum f(α) for one-dimensional sections through the dissipation field. Two operational approximations are made: first, for most of the results, a single component of the energy dissipation will be used as a representative of the total dissipation; second, we use Taylor's forzen flow hypothesis. The validity of both these approximations will be briefly assessed. We relate our results to lognormality, velocity structure functions, auto-correlation function of the dissipation rate, Kolmogorov's -5/3 law for the energy spectrum, the skewness and flatness factor of velocity derivatives, as well as to possible improvements in estimating various interface dimensions. We conclude that the multifractal approach provides a useful and unifying framework for describing the scaling properties of the turbulent dissipation field.