Title: Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept,
Abstract: To understand the self-sustenance of subcritical turbulence in spectrally
stable shear flows, we performed direct numerical simulations of homogeneous
shear turbulence for different aspect ratios of the flow domain and analyzed
the dynamical processes in Fourier space. There are no exponentially growing
modes in such flows and the turbulence is energetically supported only by the
linear growth of perturbation harmonics due to the shear flow non-normality.
This non-normality-induced, or nonmodal growth is anisotropic in spectral
space, which, in turn, leads to anisotropy of nonlinear processes in this
space. As a result, a transverse (angular) redistribution of harmonics in
Fourier space appears to be the main nonlinear process in these flows, rather
than direct or inverse cascades. We refer to this type of nonlinear
redistribution as the nonlinear transverse cascade. It is demonstrated that the
turbulence is sustained by a subtle interplay between the linear nonmodal
growth and the nonlinear transverse cascade that exemplifies a well-known
bypass scenario of subcritical turbulence. These two basic processes mainly
operate at large length scales, comparable to the domain size. Therefore, this
central, small wave number area of Fourier space is crucial in the
self-sustenance; we defined its size and labeled it as the vital area of
turbulence. Outside the vital area, the nonmodal growth and the transverse
cascade are of secondary importance. Although the cascades and the
self-sustaining process of turbulence are qualitatively the same at different
aspect ratios, the number of harmonics actively participating in this process
varies, but always remains quite large. This implies that the self-sustenance
of subcritical turbulence cannot be described by low-order models.