title: Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept.
abstract: To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as 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 is 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. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. 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: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. 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 (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.
authors.affiliation: Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden, Germany.|Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi 0179, Georgia.|Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia.
authors.forename: G
authors.initials: G
authors.lastname: Mamatsashvili
authors.affiliation: Chair of Fluid Mechanics, Universität Siegen, Siegen 57068, Germany.
authors.forename: G
authors.initials: G
authors.lastname: Khujadze
authors.affiliation: Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia.|Institute of Geophysics, Tbilisi State University, Tbilisi 0128, Georgia.
authors.forename: G
authors.initials: G
authors.lastname: Chagelishvili
authors.affiliation: School of Aeronautics, Universidad Politécnica de Madrid, Madrid 28040, Spain.
authors.forename: S
authors.initials: S
authors.lastname: Dong
authors.affiliation: School of Aeronautics, Universidad Politécnica de Madrid, Madrid 28040, Spain.
authors.forename: J
authors.initials: J
authors.lastname: Jiménez
authors.affiliation: Chair of Fluid Mechanics, Universität Siegen, Siegen 57068, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Foysi