Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence

TLDR

In rotating turbulence, the emergence of a k_h^−3 two‑dimensional spectrum parallels the Rhines spectrum seen in β‑plane dynamics. The study examines mechanisms that drive the two‑dimensionalization of large‑scale motions. Numerical simulations of forced turbulence in a rotating, triply periodic domain with three‑dimensional forcing centered at an intermediate wavenumber were performed. When the rotation rate is sufficiently high, energy is transferred upscale, producing a quasi‑two‑dimensional k^−3 spectrum dominated by cyclonic vortices at scales larger than the forcing.

Abstract

Forced turbulence in a rotating frame is studied using numerical simulations in a triply periodic box. The random forcing is three dimensional and localized about an intermediate wavenumber kf. The results show that energy is transferred to scales larger than the forcing scale when the rotation rate is large enough. The scaling of the energy spectrum approaches E(k)∝k−3 for k<kf. Almost all of the energy for k<kf lies in the two-dimensional (2D) plane perpendicular to the rotation z-axis, and thus the large-scale motions are quasi-2D with E(k)≈E(kh,kz=0), where kh and kz are, respectively, the horizontal and vertical components of the wavevector. The large scales consist of cyclonic vortices. Possible mechanisms responsible for the two-dimensionalization are discussed. The development of the 2D spectrum E(kh,kz=0)∝kh−3 is analogous to the dynamics of β-plane turbulence leading to the Rhines spectrum E(ky,kx=0)∝ky−5.