TY - JOUR

T1 - Interplay between turbulence and waves

T2 - large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence

AU - Pouquet, Annick

AU - Rosenberg, Duane

AU - Stawarz, Julia E.

N1 - Funding Information:
The work of Julia E. Stawarz was supported in part by the project UKR/STFC Grant ST/S000364/1.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - Novel features of turbulent flows have been analyzed recently, for example: (1) the possibility of an ideal invariant, such as the energy, to be transferred both to the small scales and to the large scales, in each case with a constant flux; (2) the existence of non-Gaussian wings in Probability Distribution Functions of kinetic, magnetic, and temperature fluctuations, together with their gradients, thus displaying large-scale as well as small-scale intermittency; and (3) the linear dependence on the control parameter of the effective dissipation in turbulence when non-linear eddies and waves interact. We shall briefly review these results with examples stemming from Solar Wind data, the atmosphere and the ocean with either magnetic fields, stratification, and/or rotation. In a second part, we shall examine numerically the inverse cascades of magnetic and of generalized helicity for Hall-MHD in the presence of forcing. These helical invariants in the ideal non-dissipative case involve various cross-correlations between the velocity and vorticity, the magnetic field, and the magnetic potential. For an ion inertial length larger than the forcing scale, the effect of the waves is significant. It leads to an exponential attenuation of the inverse cascade to large scales, since, through the velocity and vorticity, small scales play an increasing dynamical role for a strong Hall current.

AB - Novel features of turbulent flows have been analyzed recently, for example: (1) the possibility of an ideal invariant, such as the energy, to be transferred both to the small scales and to the large scales, in each case with a constant flux; (2) the existence of non-Gaussian wings in Probability Distribution Functions of kinetic, magnetic, and temperature fluctuations, together with their gradients, thus displaying large-scale as well as small-scale intermittency; and (3) the linear dependence on the control parameter of the effective dissipation in turbulence when non-linear eddies and waves interact. We shall briefly review these results with examples stemming from Solar Wind data, the atmosphere and the ocean with either magnetic fields, stratification, and/or rotation. In a second part, we shall examine numerically the inverse cascades of magnetic and of generalized helicity for Hall-MHD in the presence of forcing. These helical invariants in the ideal non-dissipative case involve various cross-correlations between the velocity and vorticity, the magnetic field, and the magnetic potential. For an ion inertial length larger than the forcing scale, the effect of the waves is significant. It leads to an exponential attenuation of the inverse cascade to large scales, since, through the velocity and vorticity, small scales play an increasing dynamical role for a strong Hall current.

KW - Hall-MHD

KW - Helicity

KW - Inverse cascades

KW - Turbulence

KW - Waves

UR - http://www.scopus.com/inward/record.url?scp=85089748895&partnerID=8YFLogxK

U2 - 10.1007/s12210-020-00951-5

DO - 10.1007/s12210-020-00951-5

M3 - Article

AN - SCOPUS:85089748895

VL - 31

SP - 949

EP - 961

JO - Rendiconti Lincei

JF - Rendiconti Lincei

SN - 2037-4631

IS - 4

ER -