Energy transfer in turbulence under rotation

Michele Buzzicotti, Hussein Aluie, Luca Biferale, Moritz Linkmann

Published 2017-11-19Version 1

It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by 2-dimensional interactions amongst triads lying on the 2D3C/slow manifold, namely on the Fourier-plane perpendicular to the rotation axis. The second mechanism is 3-dimensional and consists of interactions between triads with the same sign of helicity (homo-chiral). Here, we present a detailed numerical study of rotating flows using a suite of high Reynolds number direct numerical simulations (DNS) within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave-numbers close to the forcing scale is generated by increasingly dominant homo-chiral interactions which couple the 3-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave-numbers thanks to the 2-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by hetero-chiral triads and is dominated primarily by interaction within the fast manifold where $k_z\ne 0$. We further analyze the energy transfer in different regions in the real-space domain. In particular we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices.