Invariants for Correlations of Velocity Differences in Turbulent Fields

The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible representation is associated with a scalar function of $R$ which may exhibit different scaling exponents. The common practice of using moments of longitudinal and transverse fluctuations mixes different scalar functions and therefore may mix different scaling exponents. It is shown explicitly how to extract pure scaling exponents for correlations functions of arbitrary orders.