with and without effects of a magnetic field

Ph.D. Thesis Proposal by

Xiaomeng Zhai

(Advisor: Prof. P.K. Yeung)

Friday, December 15^{th}, 3pm

Boggs 1-90 (north side, 1^{st} floor)

Abstract:

Turbulence is ubiquitous in nature and engineering, and is characterized by disorderly fluctuations that span a wide range of scales in length and time, especially at high Reynolds numbers. The highly intermittent small scale motions can take extremely large amplitudes, and in the past spatial structures of the extreme events such as dissipation sheets and vortex filaments have been identified. However recent computational work on isotropic turbulence using grids points suggests a change in the topological feature of the extreme events at high Reynolds numbers. Since the extreme events are highly localized in space and possess fast dynamics, resolution effects both in space and time require closer scrutiny. In comparison, inertial range statistics are less susceptible to finite resolution. One way to study the structures of small scale quantities in the inertial range is by quantifying the degree of sign oscillations by the concept of cancellation exponent. Accurate values of cancellation exponents can help settle discrepancies in past experiments in the literature.

Compared with isotropic turbulence, in many applications body forces can lead to strong anisotropy and departures from classical descriptions. In particular electrically conducting fluids in a magnetic field are subjected to the Lorentz force of electromagnetic induction, which causes anisotropy at all scales in magnetohydrodynamic (MHD) turbulence. Previous simulations often employ cubic grids, which may not faithfully represent the highly anisotropic velocity field, especially the rapidly-growing integral length scales. Therefore it is important to simulate MHD turbulence on grids strongly elongated along the magnetic field direction to better understand the scale-dependent anisotropy evolution. Usually the anisotropy developed in the velocity field has a strong influence on the mixing of scalars, but there are only a limited number of studies of scalar mixing at low Schmidt numbers typical of liquid metals. Furthermore much remains unknown on how MHD turbulence evolves when coupled with other physical phenomena. For example some engineering equipment involves passing fluids through a contracting entry section before entering a straight conduit immersed in a magnetic field. Application of axisymmetric contraction strain in the entry section causes anisotropy, while the magnetic field can affect the subsequent relaxation of strained turbulence significantly.

In the proposed work, we use direct numerical simulations to address the issues of small scale structures in isotropic turbulence, and to study the anisotropy development in MHD turbulence. To examine the resolution effects in space and time on the extreme events of the small scales, simulations are performed at different spatial and temporal resolution. To characterize the structures of small-scale quantities in the inertial range, we quantify the degree of sign oscillations through the cancellation exponent, with a focus on the different values when computed at different dimensions. To minimize the numerical artifacts of finite domain effects when a magnetic field is applied, we consider turbulent flows on a periodic domain elongated along the magnetic field direction. Simulations of up to grid resolution have been performed to study the anisotropy development of MHD turbulence with isotropic initial conditions. Further, we plan to study scalar mixing at low Schmidt numbers, especially on how changes to energy transfers due to the magnetic field would affect mixing. Additionally in the case of MHD turbulence from initial conditions subjected to axisymmetric contractions, we will examine how the relaxation of strained turbulence is affected by the magnetic field. Dependencies on the Reynolds number and the strength of the magnetic field are to be quantified.

Committee:

Prof. P.K. Yeung – School of Aerospace Engineering (advisor)

Prof. Devesh Ranjan – School of Aerospace Engineering/Mechanical Engineering

Prof. John Wise – School of Physics

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