Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence

Measurements of the Reynolds stresses, integral lengthscales and Taylor microscales are reported for several cases of uniformly sheared turbulent flows with shear values in a range substantially wider than those of previous measurements. It is shown that such flows demonstrate a self-preserving structure, in which the dimensionless Reynolds stress ratios and the dissipation over production ratio, ε/P, remain essentially constant. Flows with sufficiently large $k_{\rm s} = (1/\overline{U_{\rm c}}){\rm d}\overline{U_1}dx_2$ have exponentially growing stresses and ε/P ≈ 0.68; a linear relationship between the coefficient in the exponentiallaw and k_s is shown to be compatible with measurements having k_s > 3. The possibility of a self-preserving structure with asymptotically constant stresses and ε/P ≈ 1.0 is also compatible with measurements, corresponding to flows with small values of k_s. The integral lengthscales appear to grow according to a power law with an exponent of about 0.8, independent of the mean shear, while the Taylor microscales, in general, approach constant values. Various attempts to scale the stresses and to predict their evolution are discussed and the applicability of Hasen's theory is scrutinized. Finally, an ‘exact’ expression for the pressure-strain rate covariance is derived and compared to some popular models.