Interplay between geostrophic vortices and inertial waves in precession-driven turbulence

Abstract

The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two dimensional (2D) columnar vortices and three dimensional (3D) inertial waves, whose relative energies depend on the precession parameter $Po$. The vortices resemble the typical condensates of geostrophic turbulence, are aligned along the rotation axis (with zero wavenumber in this direction, $k_z=0$) and are fed by the 3D waves through nonlinear transfer of energy, while the waves (with $k_z\neq0$) in turn are directly fed by the precessional instability of the background flow. The vortices themselves undergo inverse cascade of energy and exhibit anisotropy in Fourier space. For small $Po<0.1$ and sufficiently high Reynolds numbers, the typical regime for most geo- and astrophysical applications, the flow exhibits strongly oscillatory (bursty) evolution due to the alternation of vortices and small-scale waves. On the other hand, at larger $Po>0.1$ turbulence is quasi-steady with only mild fluctuations, the coexisting columnar vortices and waves in this state give rise to a split (simultaneous inverse and forward) cascade. Increasing the precession magnitude causes a reinforcement of waves relative to vortices with the energy spectrum approaching Kolmogorov scaling and, therefore, the precession mechanism counteracts the effects of the rotation.