Magnetohydrodynamic Turbulence
http://hdl.handle.net/10283/773
2020-02-28T07:03:47ZChaotic behaviour of Eulerian MHD turbulence
http://hdl.handle.net/10283/3152
Chaotic behaviour of Eulerian MHD turbulence
We study the chaos of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. We predict that the Lyapunov exponent, which measures the exponential separation of initially close solutions of the magnetohydrodynamic equations, is proportional to the inverse of the Kolmogorov microscale time and also obtain new results for this relation in hydrodynamic turbulence, specifically deriving a previously unknown co-efficient. These predictions agree with simulation results. The simulations also show a diminution of chaos from the introduction of magnetic helicity, which is expected to be eliminated at maximum helicity. Linear growth of the difference between fields was recently found in hydrodynamics and we find here that it extends to the magnetic and velocity fields, with growth rates dependent on the dissipation rate of the relevant field. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.
2018-08-10T16:37:16ZFully-resolved array of simulations investigating the influence of the magnetic Prandtl number
http://hdl.handle.net/10283/3099
Fully-resolved array of simulations investigating the influence of the magnetic Prandtl number
This dataset is for a paper which is currently in submission.
We explore the effect of the magnetic Prandtl number Pr_M on energy and dissipation in fully-resolved direct numerical simulations of steady-state, mechanically-forced homogeneous magnetohydrodynamic turbulence in the range Pr_M=1/32 to 32. We compare the spectra and show that if the simulations are not fully-resolved, the steepness of the scaling of the kinetic-to-magnetic dissipation ratio with Pr_M is overestimated. We also present results of decaying turbulence with helical and nonhelical magnetic fields, where we find nonhelical reverse spectral transfer for Pr_M<1 for the first time. The results of this systematic analysis have applications ranging from tokamak reactors to black hole accretion disks.
2018-06-15T10:56:22ZComparison of forcing functions in magnetohydrodynamics
http://hdl.handle.net/10283/2658
Comparison of forcing functions in magnetohydrodynamics
Results are presented of direct numerical simulations of incompressible, homogeneous magnetohydrodynamic turbulence without a mean magnetic field, subject to different kinetic forcing functions commonly used in the literature. Specifically, the forces are negative damping (which uses the large-scale field as a forcing function), a nonhelical random force, and a nonhelical static sinusoidal force (analogous to helical ABC forcing). The time evolution of the three ideal invariants (energy, magnetic helicity and cross helicity), the time-averaged energy spectra, the energy ratios and the dissipation ratios are examined. The effect of the number of grid points and Reynolds number on the performance of the forces is also considered. All three forces produce qualitatively similar steady states with some differences. In particular, the magnetic helicity is well-conserved in all cases but the sinusoidal method of energy injection has a tendency to introduce cross helicity into the system. Indeed, an ensemble of sinusoidally-forced simulations with identical parameters shows large variations in the cross helicity over long time periods, casting some doubt on the validity of the principle of ergodicity in systems where the injection of helicity cannot be controlled. Cross helicity can unexpectedly enter the system through the forcing function and must be carefully monitored. N.B. a description of the software which ran the simulations can be found in the PhD theses of the two people who designed and implemented the majority of it: Sam Yoffe ( https://arxiv.org/abs/1306.3408 ) and Moritz Linkmann respectively ( https://www.era.lib.ed.ac.uk/handle/1842/19572).
2017-04-14T15:47:36ZNonuniversality and finite dissipation in magnetohydrodynamic turbulence
http://hdl.handle.net/10283/772
Nonuniversality and finite dissipation in magnetohydrodynamic turbulence
This dataset contains the results of the study discussed in the paper 'Nonuniversality and finite dissipation in decaying magnetohydrodynamic turbulence': "A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cε=Cε,∞+C/Rz−+O(1/R2z−)), where Rz− is a generalized Reynolds number. The constant Cε,∞ describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of Cε,∞ is not universal. Direct numerical simulations were conducted on up to 20483 grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems." [paper abstract]
2015-05-12T15:05:02Z