Spectral properties of homogeneous magnetohydrodynamic turbulence

Abstract

Magnetohydrodynamics (MHD) is the study of how an electrically-conducting fluid interacts with a magnetic field. Many of the constituents of the universe possess a magnetic field and MHD has applications ranging from geophysical flows to solar and galactic physics; in fact, the possible generation of magnetic fields due to early-universe phase transitions makes MHD a valuable tool even in cosmology. From a more practical point of view, liquid metals, such as those required in nuclear fusion reactors, can be described by the MHD equations. In this thesis various aspects of homogeneous, incompressible MHD without a mean magnetic field are explored. This stripped-back setting facilitates the development of deeper knowledge of the fundamental energy transfer mechanisms of MHD turbulence. A complementary set of numerical and analytical results are presented, which explore the consequences of the fundamental interactions in MHD. First of all, the results of high-resolution direct numerical simulations of MHD subject to three different forcing functions are analysed in order to determine whether or not the method of energy injection affects the behaviour of the fields. Next, energy transfers between different length scales are computed and compared in cases with differing values of magnetic and cross helicity, with a view to understanding their influence on reverse energy transfer. The effect of the magnetic Prandtl number is studied in detail by varying both the kinetic and magnetic Reynolds numbers in decaying turbulence with initially large values of magnetic helicity. This allows us to distinguish large magnetic Prandtl number effects from large magnetic Reynolds number effects and small kinetic Reynolds number effects.