MHD Control Characteristics Of The Free Shear Layer

The Kelvin-Helmholtz(KH)instability is widespread in areas such as astrophysics,atomosphere,geophysics,nuclear fusion and in applications of plasma in industries.Therefore,it is very important to study the mechanism of and methods to suppress the KH instability for the engineering applications of above industries.In this dissertation,based on non-ideal MHD equations and CTU+CT algorithm,combined with third-order spatial reconstruction with limiting in the characteristic variables and HLLC/HLLD Riemann solver,the KH instability in the perfect conducting,finite conducting and anisotropic magnetized fluid are simulated respectively under different conditions.The machanisms and laws of effects of the magnetic field and physical parameters are numerically investigated.The main work and conclusions are described mainly as follows:The flow characteristics and evolution of the KH instability in perfectly conducting free shear layer under magnetic field are investigated numerically;the mechanism of the stabilizing effect of aligned magnetic field and the destabilizing effect of the shear magnetic field,as well as the dispersion relation,are revealed.The stabilizing effect of aligned magnetic field is accomplished by the transverse magnetic pressure perpendicular to the magnetic field lines and the anti-bending magnetic tension directed to the the curvature center of the magnetic field lines.The former can prevent the mixing of the fluids on both sides of the shear interface,while the latter makes the curvature of the rolled interface as zero as possible.Essentially,it is the equilibrium between Maxwell stress and Reynolds stress that results in the decrease of transverse momentum transport.The magnetic field mainly stabilizes short-wave perturbations.Small viscosity and/or slight compressibility would induce some instability even in the presence of a strong magnetic field in a certain circumstance.However,shear magnetic field plays two roles:one is to suppress to the large rolled-up structure,which is the same effect as aligned magnetic field,and the other is to induce a series of small magnetic islands on the shear interface,with merging and division in those magnetic islands,many vortices generated resulting in a new unstable flow.The instability is positively correlated with the magnetic field strength,and the greater the shear degree of the magnetic field,the stronger the instability.The flow characteristics and evolution of the KH instability in resistive fluid are studied numerically,and the effects and mechanism of the non-ideal effects including resistivity,Hall effect and ambipolar diffusion on the KH instability are shown.Resistivity causes the diffusion of magnetic fields,resulting in the separation of the fluid from the magnetic field lines.Therefore,the gradient of the magnetic field at the shear interface decreases and the magnetic energy decreases,thus reducing the transverse magnetic pressure and anti-bending magnetic tension,weakening the stabilizing effect of the magnetic field.The Hall effect does not diffuse magnetic fields,but will locally change the curvature of the magnetic field lines,which leads to the transverse magnetic pressure not effectively concentrated on the interface,thus reducing the stability of the magnetic field.In addition,the Hall effect can effectively reduce the period of the linear growth and increase the linear growth rate.The ambipolar diffusion only slightly decreases the period of the linear growth and has very little effect on the linear growth rate.After saturation,the curl of the magnetic field lines inside the cat-eyes vortex is reduced,so the magnetic field strength is reduced,but the inverse resistive diffusion caused by the ambipolar diffusion makes the magnetic filed lines at the shear interface concentrated,amplifying the magnetic field strength.Therefore,the effect of ambipolar diffusion on KH instability is not significant in early times.After saturation,because magnetic field lines is mostly destroyed from inside to outside,the stability of transverse magnetic pressure is reduced,which results in unstable flow.The study of the critical Alfvenic Mach number shows that the effect of resistivity is not significant for small Reynolds numbers(10～100),and the destabilizing effect of resistivity is obvious for large Reynolds numbers(>300000).The study of KH instability in the presence of resistivity and Hall effect shows that the flow becomes unstable,but it is more stable than the case with resistivity or Hall effect alone.The flow characteristics and evolution of the KH instability in anisotropic magnetic fluid are investigated numerically.The effects of the anisotropy of viscosity and thermal conductivity on the KH instability are revealed.The result shows that viscosity anisotropy and thermal conductivity anisotropy both have weak stabilizing effect on the KH instability,but their mechanisms are different.In the case of anisotropic viscosity,the viscosity coefficient along the magnetic filed lines is much larger than that perpendicular to the magnetic field lines,which leads to a smaller shear velocity along the shear interface during the process of the interface rolling up,resulting in the degree of curl of the interface decreasing.In this process,the viscosity makes small vorticies in the rolled up structure multiply,especially in the edge and the interior several counterclockwise small vortices are generated.These small vortices can also be merged.They could destroy the process of regular linear growth,thus making the flow stable.In the case of anisotropic thermal conductivity,at the later stage of saturation,the internal temperature is higher and the external temperature is low due to the straightening of the magnetic filed lines in the cat-eyes structure,which leads to a large-scale heat exchange process appears in the direction perpendicular to the magnetic field lines.This process effectively reduces the temperature gradient perpendicular to the magnetic field lines,thus changing the internal energy inhomogeneity across the shear interface,reducing the longitudinal kinetic energy and facilitating the stability of the flow.In the aspect of influence on coherent structures,the anisotropic viscosity makes the small-scale vortex structure with high frequency,which grows with time,decay with time.The anisotropic thermal conductivity decreases the growth or attenuation rate of the coherent structure with low frequency,and slightly increases the oscillation frequency of the secondary coherent structure with high frequency.