Drift towards isotropization during the 3D hydrodynamic turbulence onset
D. S. Agafontsev, A. S. Il'yn, A. V. Kopyev
TL;DR
The paper investigates the onset of turbulence in the incompressible 3D Euler framework, where pancake-like vorticity structures create strong anisotropy. It develops isotropy markers from Gram-matrix based statistics and tests them with high-resolution simulations that blend a shear flow with a random periodic component to control anisotropy. A key finding is that the isotropy markers drift slowly toward unity, indicating slow isotropization without triggering viscous scales, even when pancakes align preferentially along a axis, suggesting a gradual restoration of isotropy that may enable Kolmogorov-like spectral behavior under certain conditions. Together, the work provides a quantitative framework for tracking isotropy during turbulence onset and informs understanding of how isotropy emerges prior to viscous effects.
Abstract
The incompressible three-dimensional Euler equations develop very thin pancake-like regions of exponentially increasing vorticity. The characteristic thickness of such regions decreases exponentially with time, while the other two dimensions do not change considerably, making the flow near each pancake strongly anisotropic. The pancakes emerge in increasing number with time, which may enhance the anisotropy of the flow, especially if they orient similarly in space. In the present paper, we study numerically the anisotropy by analyzing the evolution of the so-called isotropy markers [Phys. Rev. Fluids 10, L022602 (2025)]. We show that these functions drift slowly towards unity, indicating the process of slow isotropization, which takes place without the viscous scales getting exited and despite the similar orientation of the emerging pancakes.