Dynamics of homogeneous shear turbulence – a key role of the nonlinear transverse cascade in the bypass concept

Author: George Mamatsashvili
Co-authors: G. Khujadze, G. Chagelishvili, S. Dong, J. Jimenez, H. Foysi
Keywords: shear flow, nonmodal growth, turbulence
Annotation:

We performed direct numerical simulations homogeneous shear turbulence to understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows. In such flows, exponentially growing modes are absent, so the turbulence can be energetically supported only by transient, or nonmodal growth mechanism due to shear flow nonnormality. We analyzed the turbulence dynamics in spectral/Fourier space for different aspect ratios of the simulation domain. Specifically, we examined the interplay of linear transient growth of Fourier harmonics and nonlinear processes that ensure the self-sustenance of turbulence. The transient growth of harmonics is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in spectral space and, as a result, the main nonlinear process is not a direct/inverse, but rather a transverse/angular redistribution of harmonics in Fourier space referred to as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by the subtle interplay of the linear transient, or nonmodal growth and the transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These processes mainly operate at large length scales, comparable to the box size. Consequently, this central, small wavenumber area of Fourier space is crucial, since the self-sustenance process is mainly concentrated there. We defined the size of this area and labeled it as the vital area. Outside the vital area, the Fourier harmonics' energy is transferred to dissipative scales by the usual direct cascade and the transient growth and transverse cascade processes are of secondary importance. Although the cascades and the self-sustaining process are qualitatively the same at different aspect ratios, the number of harmonics participating in the self-sustaining process varies with the aspect ratio, but is always quite large (36, 86 and 209 in the considered here aspect ratios). This implies that the self-sustaining process of homogeneous shear turbulence is quite complex and cannot be described by low-order models.