The effects of curvature on sheared turbulence

Abstract

The present experiments are an extension of previous studies on nearly homogeneous, parallel, shear flows and represent an attempt to study the effects of curvature on sheared turbulence in relative isolation from wall and entrainment effects. Uniformly sheared turbulence was allowed to reach a state of transverse statistical homogeneity in a straight rectangular duct: it was then passed into a curved duct, also of rectangular cross-section. The near homogeneity of the turbulence and the near uniformity of the shear were preserved. In the present experiments, the parameter S = (Uc/Rc)(dU/dn) spanned a wide range, from approximately -0.50 to over 1.0 (Uc is the centreline velocity, dU/dn the mean shear and Rc the radius of curvature on the centreline of the duct). Variation of S was achieved by using two curved tunnel sections as well as by adjusting the shear. Measurements indicate that the growth of the turbulent stresses and lengthscales was enhanced for S < 0 and suppressed for S > 0. For S > 0.05, the stresses decayed. In cases where sufficiently large total strain was achieved, the stresses seemed to grow or decay roughly exponentially and to develop in a quasi-self-preserving manner. The magnitude of the dimensionless shear stress decreased monotonically with increasing S, while, for sufficiently large positive values of S, this quantity reversed sign, to achieve the same sense as the mean shear. Measurements of the integral lengthscales and the Taylor microscales are presented and their dependence upon curvature discussed. The results in ‘mildly curved’ flows are used to derive approximate expressions for the dependence upon S of the various terms in the Reynolds stress equations, including the pressure-strain rate covariance tensor.