Abstract
Large-scale stability of a homogeneous turbulent shear flow Ū = (Sx2, 0, 0) is considered. Using a first order smoothing we have obtained the corresponding Reynolds equations. Exploiting the symmetries' property of back-ground flow we are able to obtain a complete set of modes for perturbations of unbounded flow. The flow is rigorously stable to linear disturbances of all wavenumbers. However, the intensive growth of 3-D perturbations at the inviscid stage during the finite times caused by non-zero small-scale helicity breaks the validity of the linear approximation. The growth perturbations are elongated along the basic flow. The influence of axial-symmetric helical turbulence on the evolution of large-scale perturbations of velocity is also under consideration.
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