Linearized Analysis of One-Dimensional Magnetohydrodynamic Flows

ISBN-13: 9783642460074 / Angielski / Miękka / 2012 / 122 str.

Roy M. Gundersen

Opis

Magnetohydrodynamics is concerned with the motion of electrically conducting fluids in the presence of electric or magnetic fields. Un- fortunately, the subject has a rather poorly developed experimental basis and because of the difficulties inherent in carrying out controlled laboratory experiments, the theoretical developments, in large measure, have been concerned with finding solutions to rather idealized problems. This lack of experimental basis need not become, however, a multi- megohm impedance in the line of progress in the development of a satisfactory scientific theory. While it is true that ultimately a scientific theory must agree with and, in actuality, predict physical phenomena with a reasonable degree of accuracy, such a theory must be sanctioned by its mathematical validity and consistency. Physical phenomena may be expressed precisely and quite comprehensively through the use of differential equations, and the equations formulated by LUNDQUIST and discussed by FRIEDRICHS belong to a class of equations particularly well-understood and extensively studied. This class includes, in fact, many other eminent members, the solutions of which have led to results of far-reaching scientific and technological application. Frequently, the mathematical analysis has provided the foundations and guidance necessary for further developments, and, reciprocally, the physical problems have provided, in many cases, the impetus for the development of new mathematical theories which often have evolved to an a priori unpredictable extent.

Spis treści

1. General Theory.- 1.1 Introduction.- 1.2 The Linearized Equations.- 2. Shock Propagation in Non-Uniform Ducts.- 2.1 Introductory Comments.- 2.2 Transition Relations Across Normal Shocks.- 2.3 Solution behind the Incident Shock.- 2.4 The Reflected Disturbance.- 2.5 Modified Perturbation Theory.- 2.6 Criterion for the Particle Velocity to be Unaffected by Entropy Perturbations.- 3. The Piston-Driven Shock Wave.- 3.1 Arbitrary Area Variations.- 3.2 The Piston-Driven Cylindrical Shock Wave.- 3.3 The Piston-Driven Spherical Shock Wave.- 3.4 The Integrated Shock Strength-Area Relation.- 4. Flows with Heat Addition.- 4.1 The Linearized Equations.- 4.2 Extension of Stocker’s Work.- 4.3 Modified Perturbation Theory.- 5. Simple Wave Flows.- 5.1 Introductory Comments.- 5.2 The Monatomic Fluid.- 5.3 Perturbation of a Centered Simple Wave Flow.- 5.4 Perturbation of an Arbitrary Simple Wave.- 5.5 A Class of Exact Solutions of Non-Isentropic Flow.- 6. Formation and Decay of Shock Waves.- 6.1 Introduction.- 6.2 The Simple Wave Transition.- 6.3 The Differential Equation for the Shock Path.- 6.4 Decaying Shock Wave.- 6.5 Formation of a Shock Wave.- 7. The Effects Due to an Oblique Applied Field.- 7.1 The Characteristic Form of the Governing Equations.- 7.2 Transition Relations Across Oblique Shock Waves.- 7.3 Perturbation of a Centered Simple Wave Flow.- 7.4 Perturbation of an Arbitrary Simple Wave.- References.- Appendices.- A. Principal Notation.- B. The Characteristic Form of the Basic Equations.