Effects of plane strain and rotation on homogeneous turbulence

New configurations of plane distortion based on the principle of rotation-strain coupling are examined experimentally and theoretically. The distortions cover the 'hyperbolic' domain of dominant strain and the 'elliptic' domain of dominant rotation and include the limiting case of plane shear corresponding to equal rates of strain and rotation. The measurements confirm the uniformity of the mean velocity gradients, in agreement with the theory, as well as the transverse homogeneity of the turbulent field. The action of the distortion results in a decrease of the turbulent energy decay and in a progressive anisotropization of the Reynolds stresses in the distortion plane. The rotation tends to attenuate this anisotropy. In the elliptic flow regime the turbulent quantities undergo undulatory variations due to the periodic character of this flow. The theoretical approach is based on the rapid distortion theory. Exact solutions in Fourier space are obtained by solving numerically the linearized Craya equation. The results confirm qualitatively the main tendencies observed in the experiments. The behavior of the linear pressure-strain correlations is especially analyzed.