A vortex interaction mechanism for generating energy and enstrophy fluctuations in high-symmetric turbulence

Turbulent vortex dynamics is investigated in triply periodic turbulent flow with Kida’s high symmetry (Kida, J. Phys. Soc. Japan , vol. 54, 1985, pp. 2132–2136) by means of unstable periodic motion representing both the statistical and dynamical properties of turbulence (van Veen et al. , Fluid Dyn. Res. , vol. 38, 2006, pp. 19–46). In the periodic motion, the large-scale columnar vortices, the smaller-scale vortices and the large-amplitude axial waves on the large-scale columnar vortices are detected. In terms of mutual dynamical interaction between the large-scale columnar vortices and smaller-scale vortices, we demonstrate a cyclic process of excitation of the axial waves, which leads to large-amplitude fluctuations of the total kinetic energy and enstrophy. This cyclic process is characterised by three distinct phases and is therefore reminiscent of the regeneration cycle of near-wall turbulence structures (Hamilton et al. , J. Fluid Mech. , vol. 287, 1995, pp. 317–348). Notably, such oscillatory behaviour is observed even in freely decaying turbulence as a consequence of the instantaneous energy transfer from smaller to larger scales.