# Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept

## TL;DR

This paper investigates how nonlinear transverse cascades in Fourier space sustain homogeneous shear turbulence, emphasizing the importance of nonmodal growth and anisotropic nonlinear processes in a bypass turbulence scenario.

## Contribution

It introduces the concept of the nonlinear transverse cascade as a key process in the self-sustenance of subcritical shear turbulence, supported by direct numerical simulations.

## Key findings

- Nonmodal growth drives turbulence energy in shear flows.
- Nonlinear transverse cascade redistributes harmonics angularly in Fourier space.
- Self-sustenance involves a complex interplay of linear and nonlinear processes at large scales.

## 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.