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Resolution of an Initial Shear Flow Discontinuity in One-Dimensional Hydromagnetic Flow (Classic Reprint) - Softcover
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Excerpt from Resolution of an Initial Shear Flow Discontinuity in One-Dimensional Hydromagnetic Flow
An idealized physical situation in which a shear flow discontinuity occurs is the following. Consider a layer of perfectly conducting, compresable fluid with faces transverse to the x-direction. Assume, at the initial instant, that the fluid within the layer moves uniformly in the negative y-direction, that only the fluid.within the layer is in motion, and that the pressure and density are continuous across the layer faces and are independent of x. Such an initial motion may be regarded as an idealization of a jet proceeding in the negative y-direction and much wider in the z-direction than in the x-direction. At each face of the jet we encounter a shear flow discontinuity. The waves resulting from the resolution of the shear flow discontinuity at each face will interact only after a certain time. Before this time the situation may be described by a wave motion resulting from a Single interface. It is this motion that is con sidered here.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from Resolution of an Initial Shear Flow Discontinuity in One-Dimensional Hydromagnetic Flow
An idealized physical situation in which a shear flow discontinuity occurs is the following. Consider a layer of perfectly conducting, compresable fluid with faces transverse to the x-direction. Assume, at the initial instant, that the fluid within the layer moves uniformly in the negative y-direction, that only the fluid.within the layer is in motion, and that the pressure and density are continuous across the layer faces and are independent of x. Such an initial motion may be regarded as an idealization of a jet proceeding in the negative y-direction and much wider in the z-direction than in the x-direction. At each face of the jet we encounter a shear flow discontinuity. The waves resulting from the resolution of the shear flow discontinuity at each face will interact only after a certain time. Before this time the situation may be described by a wave motion resulting from a Single interface. It is this motion that is con sidered here.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from Resolution of an Initial Shear Flow Discontinuity in One-Dimensional Hydromagnetic Flow
We are concerned here with the nonlinear one-dimensional hydromagnetic flow problem of the resolution of an initial shear flow discontinuity in a perfectly conducting, electrically neutral, compressible fluid. By one-dimensional hydromagnetic flow we mean a hydromagnetic flow in which the dependent variables, the magnetic intensity, fluid velocity, density, pressure and entropy per unit mass, are functions of one space variable, x say, and time t; no restriction need be imposed as to the presence or absence of the y- and z-components of the magnetic intensity and fluid velocity. Consider a plane surface normal to the x-axis across which a component, the y-component say, of the velocity is discontinuous and across which no fluid passes. In addition, let it be assumed that these variables are independent of x initially and, moreover, that the transverse component of the magnetic field (i.e., the component normal to the x-axis), vanishes initially. Such a flow discontinuity is referred to as a shear flow discontinuity. Since the basic hydromagnetic equations are invariant under galilean transformations we may, without loss of generality, assume that the longitudinal component of the velocity (i.e., the component parallel to the x-axis), and the z-component of the velocity also vanish and that the y-component of the velocity in the region x > 0 is equal and opposite to that in the region x < 0. Hereafter, we shall assume this to be the case. Now if the longitudinal component of the magnetic field, Hₓ, is assumed not to vanish, it can be shown that a shear flow discontinuity is not an admissible hydromagnetic contact discontinuity. The existence of an initial shear flow discontinuity in the presence of a longitudinal magnetic field must therefore be accommodated by a suitable motion of the medium. We refer to this motion as being a 'resolution' of the initial shear flow discontinuity.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Resolution of an Initial Shear Flow Discontinuity in OneDimensional Hydromagnetic Flow Classic Reprint
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Resolution of an Initial Shear Flow Discontinuity in OneDimensional Hydromagnetic Flow Classic Reprint
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Resolution of an Initial Shear Flow Discontinuity in One-Dimensional
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Paperback. Zustand: New. Print on Demand. This book introduces a resolution to an initial shear flow discontinuity in one-dimensional hydromagnetic flow. The author begins by explaining the formulation of the problem and deriving the equations of one-dimensional hydromagnetic motion, which lead to the use of hydromagnetic shocks and simple waves to describe the resolution. They then thoroughly investigate switch-on shocks and fast gas shocks, as well as slow and fast simple waves, leading to the construction of the solution to the initial discontinuity problem. The implications of these findings are then discussed, with particular attention to the behavior of the magnetic field and the nature of the motion in different flow regions. The book also investigates the dependence of pressure ratios and other quantities of interest on the parameters that characterize the state of the medium, providing numerical results and approximate expressions for specific cases. The depth of the subject is broad, including topics in gas dynamics, fluid mechanics, shock waves, magnetic fields, and the physics of plasmas. The book is a valuable reference for researchers in these fields, as well as for anyone interested in the behavior of fluids and plasmas in the presence of magnetic fields. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332093359_0
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