Abstract

We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier–Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii)–(iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence.

Highlights

  • Helicity is an invariant of the Navier–Stokes equations (NSE) in three spatial dimensions when neglecting the effects of viscous dissipation and external forcing (Moffatt & Tsinober 1992; Frisch 1995; Chen, Chen & Eyink 2003a; Alexakis & Biferale 2018)

  • In this paper we further investigate the statistical properties of the dual energy– helicity transfers by adopting a power-law multi-scale stirring mechanism, which allows us to explore three different regimes concerning the relative intensity of energy and helicity injections

  • In a regime where both small-scale energy and helicity contents are controlled by the forcing, leading to maximal-helicity flow configurations, we study the preferential concentration of isotropic helicoids (Kelvin 1872; Gustavsson & Biferale 2016), i.e. point-like particles whose dynamics is isotropic but breaks mirror symmetry

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Summary

Introduction

Helicity is an invariant of the Navier–Stokes equations (NSE) in three spatial dimensions when neglecting the effects of viscous dissipation and external forcing (Moffatt & Tsinober 1992; Frisch 1995; Chen, Chen & Eyink 2003a; Alexakis & Biferale 2018). In a regime where both small-scale energy and helicity contents are controlled by the forcing, leading to maximal-helicity flow configurations, we study the preferential concentration of isotropic helicoids (Kelvin 1872; Gustavsson & Biferale 2016), i.e. point-like particles whose dynamics is isotropic but breaks mirror symmetry. By using both direct numerical simulations (DNS) and a stochastic model for the Eulerian advecting velocity field (Gustavsson & Mehlig 2016), we show that isotropic helicoids possess highly non-trivial preferential sampling of the underlying helical flow properties depending on the particle parameters.

Helical turbulent flows
Numerical simulation
Stochastic helical flows
Helical turbulent flows: suspensions of helicoidal particles
Isotropic helicoids
Preferential sampling of vorticity and helicity
Small-scale fractal clustering
Limiting cases
Small values of Ku
Discussion and conclusions
Full Text
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