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

Abstract

We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically averaged fields. Data for the analysis are provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536 3 grid points, with Reynolds numbers between ≈1100 and ≈5100, and with moderate Rossby numbers between ≈0.06 and ≈8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation, only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of an infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.

Quantifying resonant and near-resonant interactions in rotating turbulence

“…Within the framework of the helical decomposition, Waleffe (1993) also considered the resonant triads, and pointed out that a parametric instability may be the mechanism behind the preferential transfer of energy towards quasi-two dimensional modes: the resonant condition ω(k) = ω(p) + ω(q) is more easily satisfied by modes with small vertical wavenumber, thus being preferred by the nonlinear coupling. This tendency in the energy transfer towards quasi-two dimensionalisation has been confirmed both in numerical simulations (Sen et al 2012;Horne & Mininni 2013) and in laboratory experiments (Campagne et al 2015). However, the parametric instability mechanism of Waleffe (1993) is valid for isolated triads; in a real turbulent flow, in which each triad is coupled to a miriad of other triads, it is unclear whether this is the actual mechanism responsible for the quasi-two dimensionalisation.…”

Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence

“…In comparison, measurements in 2D and 3D yield more robust results that are less biased by the presence of structures with an increased degree of spatial coherence. As a result, interpretation of experimental results obtained using 1D measures requires extra caution 14 , and higher order measures should be preferred as a rule. Second, the demonstrable correlation between the structures and cancellation exponents allows the use of cancellation exponent as a convenient tool to monitor geometrical changes.…”

“…The examples constructed above show that even simple signals can be sign-singular. In fact, sign-singularity is ubiquitous in nature, such as in more sophisticated signals in magnetohydrodynamics (MHD) [5][6][7] , solar activities [8][9][10][11] , geomagnetic field 12 , helical flows 13 , rotating turbulence 14 and aspects of classical turbulence [1][2][3] . As an example, Fig.…”

On the inverse energy transfer in rotating turbulence

“…The presence of the Coriolis force in these flows breaks isotropy [20], generates inertial waves and gives rise to the formation of large scales columnar vortices [4,21]. The resulting flows look almost bidimensional, with most of the energy accumulated in the modes perpendicular to the rotation axis, as seen in simulations [6,22] and experiments [23]. These effects happen because the nature of the nonlinear interactions is changed [24,25] with the appearance of resonant interactions due to the action of the inertial waves in the turbulent flow [26].…”