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

摘要

The relevance of two-dimensional three-components (2D3C) flows goes wellbeyond their occurrence in nature, and a deeper understanding of their dynamicsmight be also helpful in order to shed further light on the dynamics of puretwo-dimenional (2D) or three-dimensional (3D) flows and vice versa. The purposeof the present paper is to make a step in this direction through a combinationof numerical and analytical work. The analytical part is mainly concerned withthe behavior of 2D3C flows in isolation and the connection between the geometryof the nonlinear interactions and the resulting energy transfer directions.Special emphasis is given to the role of helicity. We show that a generic 2D3Cflow can be described by two stream functions corresponding to the two helicalsectors of the velocity field. The projection onto one helical sector(homochiral flow) leads to a full 3D constraint and to the inviscidconservation of the total (three dimensional) enstrophy and hence to an inversecascade of the kinetic energy of the third component also. The coupling betweenseveral 2D3C flows is studied through a set of suitably designed directnumerical simulations (DNS), where we also explore the transition between 2Dand fully 3D turbulence. In particular, we find that the coupling of three 2D3Cflows on mutually orthogonal planes subject to small-scale forcing leads tostationary 3D out-of-equilibrium dynamics at the energy containing scales. Thetransition between 2D and 3D turbulence is then explored through adding apercentage of fully 3D Fourier modes in the volume.