The flow conditions in a low attenuation electromagnetic shock tube are discussed and compared with those in pressure driven shock tubes and conventional electromagnetic shock tubes. The low attenuation electromagnetic shock tube differs from the conventional electromagnetic shock tube in that it incorporates a diaphragm separating the high pressure driver section from the low pressure expansion section. It was shown that the shock tube gives a plane shock front and a region of shock heated gas separated from the driver gas by a non-plane contact surface. The electrical conductivity of shock heated argon was measured for shock speeds of from Mach 8 to Mach 35, and downstream pressures of from 0.01 to 2.0 mm Hg, and was found to agree with theory at the higher downstream pressures but to fall below the theoretical values at the low pressures. The low values of conductivity were attributed to a non-attainment of equilibrium behind the shock front due to the greater relative importance of electron diffusion at low densities. The shock heated gas was used as the working fluid in two magnetohydrodynamic power generators. In the first the internal resistance of the generator was measured as a function of electrode area and generator current. It was concluded that at high currents a cathode spot was formed, and the measured resistances were related to a theory of cathode spot conduction. In the second generator some effects of the non-scalar conductivity of the plasma at high magnetic fields were investigated. It was shown that the values of Hall voltages in a magnetohydrodynamic generator agree with theory, and can be used to obtain an estimate of the electron density in the plasma. The reduction of the generator current by Hall currents was measured. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The action principle of field theory, usually applied only to linear theories, such as electrodynamics, is shown to be useful in the nonlinear theory of magnetohydrodynamics The well-known conservation laws are derived by utilization of invariance properties of the appropirate lagrangian In addition, a set of new conservation laws, corresponding to generalizations of the Helmholtz vortex theorem in hydrodynamics, are obtained by exploiting a certain type of gauge invariance of the magnetohydrodynamical action integral A number of formal simplifications are introduced which suggest themselves through the action principle Three problems which illustrate the resulting formulation of magnetohydrodynamics are discussed / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A discussion of probe measurement of the magnetic field in a plasma is presented with particular reference to the perturbation of the magnetic field caused by the probe. A correction procedure is developed to compensate for this perturbation. Using magnetic probes, radial variation of the current density distributions are obtained for an argon plasma in a z-pinch discharge. Initial argon pressures of 100, 250, and 500 μHg are investigated. The current density distributions are determined for 1 μsec intervals between the initiation of the discharge and the occurrence of the first pinch. These current density distributions are compared with photographic observations. The experimental results are discussed in terms of the snowplow model and the shock wave model. Mathematically, the non-linear snowplow equation is solved using an approximation technique which results in analytic solutions. The shock wave equation is solved by a graphical technique. An extension of the shock wave model is proposed for a better understanding of the experimental results. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This dissertation reported an experimental answer to the long-standing question of how three-dimensionality appears in wall-bounded magnetohydrodynamic flows and presented also an experimental study on the transition to turbulence in a confined, mostly quasi two-dimensional flow. Accordingly, it was shown the analysis of a vortex array with susceptibility to three-dimensionality, enclosed in a cubic container and a mostly, quasi two-dimensional vortex pair confined by the walls of a shallow, cylindrical container. Both containers were hermetically filled by a liquid metal fluid and subject to a constant, homogeneous magnetic field. The flow forcing was made by injecting constant electric current from one wall that intersects magnetic field lines (Hartmann wall). Flow characteristics and the presence of three-dimensionality were monitored by measuring electric potentials on either Hartmann walls that confined the liquid metal. A form of three-dimensionality termed as weak appeared through differential rotation along the axis of individual vortices, while a strong form manifested itself in vortices that do not extend from one to the other Hartmann wall. In the cubic container, this resulted into an array of novel, spectacular flow structures that were both steady and strongly three-dimensional, and, yielded to a frequency-selective breakdown of quasi two-dimensionality in chaotic and turbulent flow regimes. The mostly quasi two-dimensional flow in the shallow, cylindrical container was shown to undergo a sequence of supercritical bifurcations to turbulence triggered by boundary layer separations from the circular wall. For very high forcing, the flow reached a turbulent regime where the dissipation increased drastically. This was related to a possible transition from a laminar to a turbulent Hartmann layer.

No description available.

本論文討論了粘性依賴於密度的等熵可壓縮MHD 方程具有一般數據的整體通定性問題。它是關於可壓縮Navier-Stokes 方程整體通定性的相應推廣(參見38，48 ，73) 。具體而言，我們得到了以下新的結果。 / I:我們證明了具有形如 μ=const. >0, λ(ρ)= ρ^β, β>4/3的粘性係數的等熵可壓縮MHD 方程在二維週期域上整體光滑解的存在唯一性。其中初始密度可以包含真空，並且初始教據可以任意大。 / II 對於全空間上的初值問題，無論初始密度具有具空或者非具空遠場，在具有和I中粘性係教相同的限制條件下，我們都能證明其整體光滑解的存在唯一性。 / 這些結果基於磁場H 的任意的 Lt^∞ Lx^p先驗估計和H▽H ủ的L¹ 估計的一個但等式，它們是處理搞合的磁場和速度場的關鍵。我們充分利用了這兩點觀察和(42 ， 46 ， 73) 中針對NavierStokes 方程提出的框架獲得了密度的一致上界并進一步得到了高階估計。 / In this thesis, we study the global well-posedness of solutions to the compressible MHD equations with density-dependent viscosity coefficients with general initial data. These results are the generalization of the corresponding ones for the compressible Navier-Stokes equations [42, 56, 83]. We obtain the following new results. / I.We show that the global existence and uniqueness of classical solutions to the isentropic compressible MHD equations with the viscosity coefficients satisfying μ=const. >0, λ(ρ)= ρ^β, β>4/3 on the two-dimensional torus. The initial density is allowed to vanish and the initial data can be arbitrary large. / II. We establish the same result for the Cauchy problem of the compressible MHD equations under the same assumptions, whenever the initial density with vacuum or nonvacuum as far fields. / These results based on the arbitrary Lt^∞ Lx^p a priori estimates of magnetic field H and a new identity for the L¹ estimates of H▽H ủ which are crucial to deal with the strongly coupled magnetic field with the velocity field. We take full advantage of these two key observations and framework proposed in [42, 56, 83] for the compressible Navier-Stokes equations to obtain the uniform upper bound of the density and further derive higher order estimates. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Mei, Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 79-88). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.3 / Chapter 2 --- Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum on T² --- p.13 / Chapter 2.1 --- Main Results --- p.14 / Chapter 2.2 --- Preliminaries --- p.15 / Chapter 2.3 --- A priori estimates --- p.18 / Chapter 2.4 --- Higher order estimates --- p.36 / Chapter 2.5 --- Proof of the Theorem --- p.54 / Chapter 3 --- Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum on R² --- p.57 / Chapter 3.1 --- Main Results --- p.58 / Chapter 3.2 --- Preliminaries --- p.60 / Chapter 3.3 --- A priori estimates --- p.64 / Chapter 3.4 --- Proof of main results --- p.73 / Chapter 4 --- Discussions and Future Work --- p.77 / Bibliography --- p.78

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 165-170).

No description available.

Aspects of thermal convection in the Earth's fluid core in the presence of a strong azimuthal magnetic field may be understood by considering a horizontal plane layer, rotating about the vertical z axis, with gravity acting downwards and containing an applied magnetic field aligned in the y (azimuthal) direction. Since the OMB is not smooth, the effects of adding bumps (with axes perpendicular to the applied magnetic field) to the top boundary of the layer are investigated in the magnetogeostrophic limit. The arbitrary geostrophic flow that arises under this limit is evaluated using a modified Taylor constraint. The bumps distort the isotherms so that they are not aligned with equipotential surfaces, leading to an imperfect configuration. This means that a hydrostatic balance is not possible, and motion ensues. This motion takes the form of a steady transverse convection roll, with axis parallel to the bumps. The roll exists for all values of the Rayleigh number, except that value for which the corresponding homogeneous problem in the standard plane layer has a solution. The roll obeys Taylor's constraint, and has no associated geostrophic flow. The stability of this roll to perturbation by oblique rolls (which are preferred for 0(1) values of the Elsasser number) is considered. It is found that the most unstable linear mode consists of a pair of these oblique rolls, aligned so that no geostrophic flow is accelerated by their interaction with the basic state. Hence, the stability results obtained here are identical to those found by perturbing the hydrostatic conduction solution with oblique rolls in the standard layer. Finally, the nonlinear evolution through the Ekman regime of these linear instabilities is considered. It is found that the nonlinear convection behaves similarly to mean field dynamo models which incorporate a geostrophic nonlinearity. Various types of Ekman solution are found, and evolution to Taylor states is observed.

Thesis (M.S.)--University of Wisconsin--Madison, 1966. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 40-41)