Scaling and energy transfer in rotating turbulence

Abstract

The inertial-range properties of quasi-stationary hydrodynamic turbulence under solid-body rotation are studied via high-resolution direct numerical simulations. For strong rotation the nonlinear energy cascade exhibits depletion and a pronounced anisotropy with the energy flux proceeding mainly perpendicularly to the rotation axis. This corresponds to a transition towards a quasi-twodimensional flow similar to a linear Taylor-Proudman state. In contrast to the energy spectrum along the rotation axis which does not scale self-similarly, the perpendicular spectrum displays an inertial range with k −2 ⊥ -behavior. A new phenomenology gives a rationale for the observations. The scaling exponents ζp of structure functions up to order p = 8 measured perpendicular to the rotation axis indicate reduced intermittency with increasing rotation rate. The proposed phenomenology is consistent with the inferred asymptotic non-intermittent behavior ζp = p/2.The inherent properties of turbulence in a rotating reference frame are important for, e.g., the dynamics of atmosphere and oceans, liquid planetary cores, and engineering problems. The nonlinear spectral transfer of energy by the direct turbulent cascade and the associated energy spectrum are particularly interesting due to their direct connection to the dynamical processes governing rotating turbulence. Most of the available experimental data [1,2,3,4,5] yields no conclusive information on the expected self-similar scaling of the energy spectrum in the inertial range of scales and its dependence on the rotation frequency Ω. Although recent experiments [6,7,8] have shed some light on these issues, the scaling of two-point statistics in rotating turbulence remains a controversial topic.Direct numerical simulations [9,10,11,12,13,14,15,16] and large-eddy simulations, see e.g. [17,18,19], have been carried out only at low and moderate Reynolds numbers precluding clear scaling observations. Nevertheless, most of the cited works agree in that the nonlinear spectral transfer of energy to smaller scales diminishes with growing Ω, accompanied by a transition of the flow towards a quasi-two-dimensional state perpendicular to the fixed rotation axis, Ω. The transition manifests itself in an increasing ratio of integral length scales parallel and perpendicular to Ω = Ωê 3 , defined as L i,j = L∞ 0dℓ v i (r)v i (r + ℓê j ) / v 2 i (r) , L ∞ representing the largest possible distance between two points in the simulation volume and ℓ denoting the respective space increment.This Letter presents high-resolution direct numerical simulations of incompressible rotating homogeneous turbulence driven at largest scales and proposes a phenomenology of the energy cascade which suggests a physical explanation for the observed attenuation of nonlinear spectral transfer under the influence of rotation. In addition, the model gives a rationale for the observed trend towards two-dimensionality in rapidly rotating turbulence which is corroborated by the simulations. The scaling of two-point structure fu...

On the decrease of intermittency in decaying rotating turbulence

“…ζ 2 = 1) and linear higher-order exponents ζ q = q/2. In a Direct Numerical Simulation (DNS) of rotating turbulence with a large-scale isotropic forcing, Müller and Thiele 2 have observed reduced intermittency, also characterized with ζ 2 1, but higher-order exponents ζ q intermediate between q/2 and the values usually found in classical (intermittent) 3D turbulence. Those observations are in qualitative agreement with the increase of ζ q reported by Simand 9 from hot-wire measurements in the vicinity of a strong vortex, although no clear separation between a constant background rotation and an otherwise homogeneous turbulence advected by the rotation can be defined in this geometry.…”

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

“…(16). As an example, for run T3, and using the value of h obtained from numerical simulations of nonhelical rotating turbulence (h ≈ 1/2; see [12,13] Leaving aside the fractal dimension, several things are worth pointing out from the values of the cancellation exponent obtained. As in the case of the vertical velocity, the vertical vorticity shows signs of being sign-singular in the limit of an infinite Reynolds number.…”

“…The turbulent regime, resulting from the predominance of nonlinear interactions over viscous dissipation, is present in numerous flows in nature, such as in geophysical and astrophysical flows. The ratio of the amplitude of these two processes is described through the Reynolds number Re, which can take values as large as Re ≈ 10 8 or higher in the atmosphere and in the oceans [1], and Re ≈ 10 12 or higher in astrophysics [2]. While turbulence is often associated with very complicated and disordered flows, that is the case only for isotropic and homogeneous turbulence.…”

“…However, turbulent flows tend also to be intermittent [12,13]. Intermittency is caused by the presence of structures in the flow at different scales, highly localized in space and time.…”

“…While there are many tools to characterize intermittency in isotropic and homogeneous flows, its study in anisotropic flows is less developed. Numerical simulations and experiments indicate that rotating turbulence is less intermittent than isotropic and homogeneous turbulence [9,12,[14][15][16]. However, for rotating flows, it has been argued that the observed scaling laws may actually be spurious and the result of applying methods devised for isotropic turbulence to anisotropic flows [17].…”