## Hydrodynamic and magnetohydrodynamic turbulence : some numerical experiments

##### Doctoral thesis

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http://hdl.handle.net/11250/228428##### Issue date

2004##### Metadata

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##### Abstract

This thesis consists of a brief introduction to hydrodynamics and magnetohydrodynamics, followed by five articles that address different aspects of hydrodynamic and magnetohydrodynamic turbulence.
Paper A: Bottleneck effect in three-dimensional turbulence simulations
Numerical simulations show that the energy spectra of turbulent flows are shallower than k-5/3 near the dissipation wave number. The same effect, which is known as the "bottleneck
Paper B: Self-similar scaling in decaying numerical turbulence
It has recently been suggested (P. D. Ditlevsen, M. H. Jensen, and P. Olesen, eprint nlin.CD/0205055), that the energy spectrum for decaying hydrodynamic turbulence can described by
E(k, t, v) = kqg(kta; vtb),
where the scaling function g has only two arguments, and the parameters a and b are fully determined by the slope of the infrared spectrum of the initial field. In the
Paper C: Delayed correlation between turbulent energy injection and dissipation
The "zeroth law" of turbulence states that: for low enough viscosities the mean kinetic energy dissipation rate is finite and independent of viscosity (or equivalently, the dimensionless mean kinetic energy dissipation rateCε is a constant of order unity independent of the the Reynolds number in the high Reynolds number limit). Even though this idea is widely accepted and is a fundamental assumption in theCε from numerical simulations of isotropic3 grid points and find that a strong Taylor microscale Reynolds number (Re¸) dependence of Cε abates when Re¸ ≈ 100 after whichCε scatter in the range between 0.3 - 0.7, but that the data points collapse if we account for theCε. Not accounting for this time lag may explain the scatter in previously published results.
Paper D: Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations
In the fourth paper, the turbulent kinematic viscosity νt and the turbulent magnetic diffusivity ηt are determined from the decay rates of large scale velocity and magnetic fields in forced turbulence simulations. We find that the turbulent magnetic Prandtl number ν t/ηt is close to unity, regardless of the value of the microscopic magnetic Prandtl number ν /η, when the magnetic field is weak. When the field is strong, on the other hand, we show that ηt is quenched. The quenching for helical fields is stronger than for non-helical fields and can be described by a dynamical quenching formula.
Paper E Relaxation of writhe and twist of a bi-helical magnetic field
In the final paper, we study the decay of magnetic helicity in bi-helical magnetic fields, i.e., magnetic fields that have opposite helicity at small and large scales. We see that the positive and negative contributions of the