Scale-by-scale budget and similarity laws for shear turbulence

Abstract

Turbulent shear flows, such as those occurring in the wall region of turbulent boundary layers, show a substantial increase of intermittency in comparison with isotropic conditions. This suggests a close link between anisotropy and intermittency. However, a rigorous statistical description of anisotropic flows is, in most cases, hampered by the inhomogeneity of the field. This difficulty is absent for homogeneous shear flow. For this flow the scale-by-scale budget is discussed here by using the appropriate form of the Kámán–Howarth equation, to determine the range of scales where the shear is dominant. The resulting generalization of the four-fifths law is then used to extend to shear-dominated flows the Kolmogorov–Oboukhov theory of intermittency. The procedure leads naturally to the formulation of generalized structure functions, and the description of intermittency thus obtained reduces to the K62 theory for vanishing shear. The intermittency corrections to the scaling exponents are related to the moments of the coarse-grained energy dissipation field. Numerical experiments give indications that the dissipation field is statistically unaffected by the shear, supporting the conjecture that the intermittency corrections are universal. This observation together with the present reformulation of the theory gives a reason for the increased intermittency observed in the classical longitudinal velocity increments.