Self-organisation processes in (magneto)hydrodynamic turbulence
Linkmann, Moritz Frederik Leon
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Self-organising processes occurring in isotropic turbulence and homogeneous magnetohydrodynamic (MHD) turbulence are investigated in relation to the stability of helical flow structures. A stability analysis of helical triad interactions shows that compared to hydrodynamics, equilibria of the triadic evolution equations have more instabilities with respect to perturbations on scales larger than the characteristic scale of the system. Some of these instabilities can be mapped to Stretch-Twist-Fold dynamo action and others to the inverse cascade of magnetic helicity. High levels of cross-helicity are found to constrain small-scale instabilities more than large scale instabilities and are thus expected to have an asymmetric damping effect on forward and inverse energy transfer. Results from a numerical investigation into the influence of helicity on energy transfer and dissipation are consistent with this observation. The numerical work also confirms the predictions of an approximate method describing the Reynolds number dependence of the dimensionless dissipation coefficient for MHD turbulence. These predictions are complemented by the derivation of mathematically rigorous upper bounds on the dissipation rates of total energy and cross-helicity in terms of applied external forces. Large-scale helical flows are also found to emerge in relaminarisation events in direct numerical simulations of isotropic hydrodynamic turbulence at low Reynolds number, where the turbulent fluctuations suddenly collapse in favour of a large-scale helical flow, which was identified as a phase-shifted ABC-flow. A statistical investigation shows similarities to relaminarisation of localised turbulence in wall-bounded parallel shear flows. The turbulent states have an exponential survival probability indicating a memoryless process with a characteristic lifetime, which is found to depend super-exponentially on Reynolds number akin to well-established results for pipe and plane Couette flow. These and further similarites suggest that the phase space dynamics of isotropic turbulence and wall-bounded shear flows are qualitatively similar and that the relaminarisation of isotropic turbulence can also be explained by the escape from a chaotic saddle.