Different cascade speeds for longitudinal and transverse velocity increments of small-scale turbulence

We address the problem of differences between longitudinal and transverse velocity increments in isotropic small scale turbulence. The relationship of these two quantities is analyzed experimentally by means of stochastic Markovian processes leading to a phenomenological Fokker-Planck equation from which a generalization of the Karman equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the differences in the scaling properties of these two structure functions.