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Statistical measures of hydrodynamics

Since the dynamic equations for turbulent fluids generally show an unstable behaviour, it is practical to use statistical measures of the velocity field rather than trying to make exact predictions.

Most theories for turbulence  are based on Kolmogorov's  definitions of "homogeneous" and "homogeneous isotropic" turbulence [10]. These definitions are purely statistical, and basically impossible to test for an experiment, but Kolmogorov argues that the conditions typically are fulfilled in a small region far from the border of the system ("small" and "far" as compared to the length scale at which energy is pumped into the system). Assuming that a fluid system is homogeneous isotropic turbulent and that the average behaviour only depends on the average energy dissipation in the system, it is possible to derive a simple relation between the average energy dissipation, tex2html_wrap_inline4341, velocity differences between particles separated some distance, tex2html_wrap_inline4343, and that distance, R.