Rotating helical turbulence. II. Intermittency, scale invariance, and structures

Abstract

We study the intermittency properties of the energy and helicity cascades in two 1536 3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and nonintermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at very small scales in the flow. Finally, we observe the juxtaposition in space of strong laminar and persistent helical columns next to time-varying vortex tangles, the former being associated with the self-similarity of energy and the latter with the intermittency of helicity.

An adjoint-based approach for finding invariant solutions of Navier–Stokes equations

“…Such rare, extreme events are usually referred to as temporal intermittency and are ubiquitous in turbulent fluid flow (see, e.g., Batchelor & Townsend (1949); Sreenivasan & Antonia (1997)). Non-Gaussian probability distribu-tion of turbulent quantities are a footprint of intermittency that produces the heavy tails of the distribution functions (Frisch 1996;Mininni & Pouquet 2010).…”

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

“…However, note that unlike the case of negligible rotation, the runs with and without helicity show different scaling laws for u z (compare κ = 0.35 ± 0.04 in run A2 with κ = 0.7 ± 0.1 in run T2). This difference can be understood because helical and nonhelical rotating flows are known to follow different scaling laws (i.e., they have different Hölder exponents; see [11]), and because passive scalars advected by those flows also have different scaling as a result [44].…”

“…In rotating turbulent flows, quadratic quantities in the fields, such as the energy, the helicity, and the enstrophy, are often characterized with isotropic and anisotropic spectra [5,8,9] (or, equivalently, with second-order structure functions [10,11]) following power laws in the inertial range. However, turbulent flows tend also to be intermittent [12,13].…”

Nonlinear energy transfers and phase diagrams for geostrophically balanced rotating-stratified flows

“…In spite of the fluctuating nature of the flow, coherent structures appear at large scales in many cases. Two-dimensional turbulence is a prototypical situation where large scale coherent structures emerge [2,3], but this also happens in different contexts, for instance in three-dimensional flows in the presence of rotation [4,5]. Geophysical flows constitute a vivid illustration of the coexistence between small-scale turbulence and long-lived structures and mean flows up to the planetary scale.…”