The distortion of turbulence by general uniform irrotational strain

Abstract

This paper describes the measured response of grid turbulence to three limiting types of uniform homogeneous strain: plane straining, axisymmetric elongation and axisymmetric flattening. Straining was achieved by allowing the turbulence to be convected through suitable distorting ducts; the maximum strain ratios were 5·8, 6·0 and 2·3, respectively. An attempt is made, using rapid-distortion theory, to specify an effective strain which accounts for the initial anisotropy of the grid turbulence; in the experiments, this effect was most important for the third species of strain. The maximum effective strain ratios were calculated as 4·05, 7·2 and 2·75, respectively. The rapid-distortion results are able to describe several features of the response of the turbulence with good accuracy: (i) the variation of total turbulence energy through the experimental ducts; (ii) the tendency of one component (that in the direction of the (larger) negative strain) to contain one-half of the turbulence energy after only moderate straining; and (iii) the changes in dimensionless structure parameters composed of ratios of component intensities. The first kind of prediction requires that the concurrent decay be specified in a simple way; (ii) and (iii) require that the initial anisotropy be taken into account. The predictions (iii) are generally less accurate than the others. The degree of success achieved by the rapid-distortion hypo-thesis is rather surprising, since the strain rates in the experiments were not as large as those for which the theory might have been expected to be valid. It is concluded that successful models of turbulence must provide a vorticity amplification essentially like that of rapid-distortion theory. However, the simple distorting flows considered here may not provide severe tests of more refined models, since many features of the response have already been accounted for.