Transition from non-swirling to swirling axisymmetric turbulence

Abstract

Strictly axisymmetric turbulence, i.e., turbulence governed by the Navier-Stokes equations modified such that the flow is invariant in the azimuthal direction, is a system intermediate between two-and three-dimensional turbulence. We investigate statistically steady states of this system by direct numerical simulation using a forcing protocol, which allows the injected energy in the toroidal and in the poloidal directions to be tuned independently. A sharp transition between a two-dimensional two-component (2D2C, nonswirling) flow and a two-dimensional three-component (2D3C, swirling) flow is observed. We derive a statistical model which reproduces this transition.

Transition from axisymmetric to three-dimensional turbulence

“…The theoretical predictions of this system were shown to be in qualitative agreement with experimental measurements of a stirred turbulent wouter.bos@ec-lyon.fr flow in a cylinder, which is only axisymmetric on average [18,19]. This success inspired further theoretical studies of the axisymmetric Euler system [20][21][22][23], and recently the first numerical simulations of strictly axisymmetric turbulence [24][25][26].…”

“…The most recent of these investigations [26] , in which a linear forcing protocol is used, showed that two very different types of flows can be observed in the axisymmetric system, depending on the forcing anisotropy. When only the poloidal components of the flow are forced, a purely poloidal flow is observed with features typical of twodimensional two-component (2D-2C) turbulence, such as an inverse energy cascade and coherent structures.…”

“…First, how robust is the bifurcation from a purely poloidal (2D2C) flow to a three-dimensional three component flow when axisymmetry is not perfectly satisfied. Secondly, can we model this effect on the level of the energy balance, as we did for the purely axisymmetric case in [26]?…”

“…The axis is in the z-direction, the radial direction is r and the azimuthal direction θ. In [26] we considered the dynamics of purely axisymmetric turbulence in such a geometry. In particular, we considered the influence of the forcing anisotropy on the dynamics using a linear forcing protocol and varying the relative poloidal and toroidal forcing-strengths.…”

Three-dimensional turbulence without vortex stretching

“…2010; Qu, Bos & Naso 2017; Qin et al. 2020), or thin-layer turbulence (Celani, Musacchio & Vincenzi 2010; Benavides & Alexakis 2017; Favier, Guervilly & Knobloch 2019).…”