Sub-grid Scale Modelling of Compressible Magnetohydrodynamic Turbulence: Derivation and A Priori Analysis

by Dimitar Georgiev Vlaykov
Doctoral thesis
Date of Examination:2015-09-22
Date of issue:2015-12-11
Advisor:Dr. Wolfram Schmidth
Referee:Dr. Wolfram Schmidth
Referee:Prof. Dr. Jens Niemeyer
Referee:Prof. Dr. Christian Klingenberg
Persistent Address: http://dx.doi.org/10.53846/goediss-5427

 

 

Files in this item

Name:master_rev1_flat.pdf
Size:17.7Mb
Format:PDF

The following license files are associated with this item:

Abstract

English

Turbulence is one of the oldest and trickiest unsolved problems in our understanding of the universe. The addition of magnetic fields increases its complexity exorbitantly. There are numerous astrophysical examples where the turbulent dynamics of magnetised plasma is critical, from the largest to the smallest scales: it may hold the key to explaining the amplification of the magnification fields on galactic and super-galactic scales through small-scale dynamos, the coronal heating through turbulent reconnection, the self-regulation of star formation rate through turbulent support, et cetera. Due to the large degree of non-linearity of turbulence, numerical simulations are a preferred tool to address many of these problems. In the astrophysical context, direct numerical simulations of compressible magnetohydrodynamic turbulence, the simplest theory which contains all the basic physical ingredients, are often computationally intractable due to the prohibitively large dynamical range between the dissipative and integral scales. The finite numerical resources impose a grid with finite resolution below which no self-consistent information is computable. In order to incorporate the effects of the sub-grid scale dynamics, one needs to provide a physically justified model. The purpose of this thesis is to develop a self-consistent model which is faithful to the sub-grid scale dynamics of compressible magnetohydrodynamic turbulence. This is performed by means of a priori analysis of pre-existing data. The data has sufficient resolution for a well delineated power-law scaling, i.e. turbulent, range in the energy spectrum. An attempt is made to identify and investigate critical properties of the sub-grid scale dynamics in the simulations of developed statistically homogeneous, isotropic and stationary compressible magnetohydrodynamic turbulence. The proposed model is developed based on a deconvolution approach. It is validated a priori against the data and alternative models currently in circulation based on a set of dynamical and geometrical, frame-independent diagnostic fields.
Keywords: Magnetohydrodynamics; Turbulence; Large-eddy simulations; Modelling; Compressibility; A priori analysis; Turbulent closures
 
Statistik