The effect of uniform distortion on weak homogeneous turbulence

Abstract

The behaviour of weak homogeneous turbulence subjected to a uniform distortion is studied by means of linearized equations that include the effect of inertial interaction between the mean flow and the turbulent fluctuations and of viscous dissipation. Three particular cases of distortion are investigated in varying degrees of detail; those of uniform rotation, uniform shear, and uniform irrotational distortion. For the first two, the total energy associated with the turbulence is found to decay, but for the third it is found in general to increase without limit. A general solution in terms of the spectrum functions for the restricted case of irrotational distortions is given, particular consideration being paid to the asymptotic limits approached as the distortions (not necessarily the rates of distortion) become large. These show that for an arbitrary initial turbulent spectrum the asymptotic rates of growth are functions of the precise geometrical nature of the distortion, of an integral parameter of the initial spectrum function, of a Reynolds number based on the rate of distortion and the length scale of the initial turbulence, and of the contraction. A particular example, that of initially isotropic turbulence in its final period of decay subjected to an axisymmetric distortion, is worked out in detail and te solution (described in terms of mean turbulent intensities) displayed graphically for several values of the Reynolds number.