Effects of the Coriolis force in inhomogeneous rotating turbulence

The effects of the Coriolis force in inhomogeneous rotating turbulence are studied in the paper. Linear analyses and numerical simulations both reveal that energy is transported to the slowly rotating fields, and the energy distribution is proportional to omega(-2)(3) (x(3)). The scale energy is almost spatially self-similar, and the inverse cascade is reduced by inhomogeneous rotation. The corresponding evolution equation of the scale energy, i.e., the generalized Kolmogorov equation, is calculated to study the scale transport process in the presence of inhomogeneity. The equation is reduced to twice the energy transport equation at sufficiently large scales, which is verified by numerical results. In addition, the results reveal the dominant role of the corresponding pressure of the Coriolis force in the spatial energy transport. An extra turbulent convention effect in r-space solely in slowly rotating fields is also recognized. It can be associated with the small-scale structures with strong negative vorticity, whose formation mechanism is similar to rotating condensates. Finally, by vortex dynamic analyses, we find that the corresponding pressure of the Coriolis force transports energy by vorticity tube shrinking and thickening. The effects of the Coriolis force can be divided into two components: one is related to the gradient of rotation, and the other is associated with the strength of rotation.

Automated summary

This paper investigates the effects of the Coriolis force in inhomogeneous rotating turbulence. The results from linear analyses and numerical simulations show that energy is transported to slowly rotating fields, with the energy distribution being inversely proportional to the cube of the rotation speed. The scale energy exhibits spatial self-similarity, but the inhomogeneous rotation reduces the inverse cascade. The corresponding evolution equation, known as the generalized Kolmogorov equation, is derived to study the scale transport process. It is found that the equation reduces to twice the energy transport equation at sufficiently large scales, as confirmed by the numerical results. The dominant role of the corresponding pressure of the Coriolis force in spatial energy transport is revealed, along with the recognition of an additional turbulent convective effect in slowly rotating fields.