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

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.

Large-scale anisotropy in stably stratified rotating flows

“…Direct numerical simulations have shown that rotating flows in finite domains can develop inverse cascades of energy (see, e.g., [34,35]), and recent experiments have observed the same phenomena [36]. In the case of stratified flows, the situation is less clear.…”

Dimensional transition in rotating turbulence

“…In the strongly rotating limit, energy transfer among scales is supposedly dominated by resonant triad interactions between inertial waves [22]. Even though such interactions can move energy towards the 2D plane [17], triadic resonance cannot transfer energy into/out of the k z = 0 plane, which, in fact, constitutes a closed resonant set. If only interactions among resonant triads are allowed, 2D modes should thus be dynamically decoupled from 3D modes [18,19].…”

“…Experiments of decaying turbulence in rotating tanks show the growth of length scales aligned with the rotation axis, giving evidence that turbulence developing in rotating systems is highly anisotropic. Both linear [14,15] and nonlinear [16,17] mechanisms have been advocated to explain the observed growth. Numerical simulations of rotating flows have also indicated a general trend towards two-dimensionalization [8,17] and some studies [9] have reported a split of the energy cascade into a downscale and an upscale process.…”

“…Both linear [14,15] and nonlinear [16,17] mechanisms have been advocated to explain the observed growth. Numerical simulations of rotating flows have also indicated a general trend towards two-dimensionalization [8,17] and some studies [9] have reported a split of the energy cascade into a downscale and an upscale process. Other studies [18] have found that, as the rotation rate increases, the flows exhibit a dynamics very similar to what is found in a 2D system, with the vertical * Corresponding author: deusebio@mech.kth.se velocity behaving as a passive scalar [19].…”

Experiments on rapidly rotating turbulent flows

“…[25][26][27][28][29] Other effects of rotation are two dimensionalization, easily inferred from increased integral length scales along the axis of rotation, and a major reduction of the high wave number part of the radial energy spectrum. It should be emphasized here that most issues discussed so far by numerical studies mainly concern rotating statistically homogeneous turbulence.…”