From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows

Abstract

The relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure two-dimenional (2D) or three-dimensional (3D) flows and vice versa. The purpose of the present paper is to make a step in this direction through a combination of numerical and analytical work. The analytical part is mainly concerned with the behavior of 2D3C flows in isolation and the connection between the geometry of the nonlinear interactions and the resulting energy transfer directions. Special emphasis is given to the role of helicity. We show that a generic 2D3C flow can be described by two stream functions corresponding to the two helical sectors of the velocity field. The projection onto one helical sector (homochiral flow) leads to a full 3D constraint and to the inviscid conservation of the total (three dimensional) enstrophy and hence to an inverse cascade of the kinetic energy of the third component also. The coupling between several 2D3C flows is studied through a set of suitably designed direct numerical simulations (DNS), where we also explore the transition between 2D and fully 3D turbulence. In particular, we find that the coupling of three 2D3C flows on mutually orthogonal planes subject to smallscale forcing leads to stationary 3D out-of-equilibrium dynamics at the energy containing scales. The transition between 2D and 3D turbulence is then explored through adding a percentage of fully 3D Fourier modes in the volume.

On the inverse energy transfer in rotating turbulence

“…So while the total flux is zero, this is achieved by the dynamical balance of the channels that bring energy forwards (the heterochiral) and the ones that bring it backwards (the homochiral). The same phenomenon has been observed in flows composed by a combination of 2D3C (two dimension, three component) flows [44]. The amplitude and range of modes that are involved in this flux balance does depend slightly on the rotation rate, with simulation PRJ-A3 being the one with the largest number of modes that had non-zero flux in the homo and heterochiral channels.…”

“…If resonant interactions can make the energy transfer anisotropic, aren't they also contributing to the inverse transfer of energy? Moreover, it has been shown that even in fully homogeneous and isotropic three dimensional turbulence, there are channels that take energy backwards [14,15], that the action of these channels can be enhanced in different geometries [44], and that these channels can couple the 2D and 3D modes in rotating turbulence [36]. This adds a further avenue to explore.…”

Cascades of energy and helicity in axisymmetric turbulence

“…The fact that no additional friction is required to prevent the energy from accumulating at large scales may also be explained by alternative mechanisms. Scenarios according to which simultaneous upward and downward cascades coexist were in particular recently evidenced in 2D3C flows [28] but do not need to be invoked here to explain the damping because of the presence of walls. Figure 2(b) shows typical instantaneous flow fields in the stationary state.…”

Nonuniversal behaviour of helical two-dimensional three-component turbulence

“…As mentioned above, Π HO + (k) and Π HO − (k) contribute to a subleading inverse energy transfer even in 3D. Their combined contribution is the total homochiral flux [18,36] Π HO (k) = Π HO…”