Numerical Investigation Of Energy Cascades In Hall MHD Turbulence

Magnetohydrodynamic turbulence is a common phenomenon in natural environments such as the space and the interior of the Earth.Magnetohydrodynamics,or MHD,is a physical model describing the evolution of conducting fluid and the surrounding magnetic field while both physical fields interact with each other.The effect induced by the relative motions between ions and electrons can be depicted by MHD with the addition of Hall term.However,previous studies of Hall MHD turbulence remain rare.In this thesis,numerical investigations of global statistics,intermittency,and interscale energy transfer in Hall MHD turbulence have been conducted.Without changing other computational parameters,we performed direct numerical simulations of threedimensional forcing homogeneous isotropic Hall MHD turbulence using Fourier pseudospectral method with five different Hall parameters,? = 0.00,0.01,0.05,0.10,0.20.The content of this thesis mainly consists of three parts.In the first part,we analyzed the numerical data from a statistical viewpoint.Our results show that,the kinetic energy spectrum of Hall MHD turbulence remains insensitive to the change of the Hall parameter while there exists an accumulation of magnetic energy in small scales with the increasing Hall parameter,revealed by the magnetic energy spectrum of Hall MHD turbulence.Based on the results of probability distribution functions,cumulative distribution functions,and scale-dependent kurtosis of vorticity and current density field in Hall MHD turbulence,we can conclude that Hall effect restrains the formation of small-scale current density structures,resulting in the decline of intermittency of current density.Meanwhile,the same analysis also shows that the increasing Hall parameter has no monotonical influence on the intermittency of vorticity.In the second part,we analyzed the inter-scale energy transfer of Hall MHD turbulence in Fourier spectral space.By computing spectral energy fluxes in the large-scale energy equations of Hall MHD,we found that both forward and inverse transfers can be observed in the inter-scale magnetic energy transfer induced by the Hall effect.Then,we decomposed the Hall term into the following nonlinear terms:b · ?j and j · ?b.Spectral energy flux and shell-to-shell energy transfer reveal that there exist two kinds of energy transfers with different directions and scales owing to the different physical processes behind these nonlinear terms.In the third part,we analyzed the inter-scale energy transfer in Hall MHD turbulence in physical space using a space-filtering technique.We derived the physical-space largescale energy equations in Hall MHD and investigated the statistical property of subgridscale(SGS)fluxes numerically.Dependence of SGS energy fluxes on the strength of the Hall effect shows that SGS flux induced by the Hall effect has very strong intermittency.Comparing the isosurfaces of SGS energy fluxes and physical fields,we observed a potential connection between these variables,which was quantified by computing their cross-correlation functions.