Hydrodynamical theory of magnetoplasma excitations in an antidot system

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

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A hydrodynamical theory of conservative bounded density currents

Journal of Fluid Mechanics ◽

10.1017/s0022112089000091 ◽

1989 ◽

Vol 198 (-1) ◽

pp. 177 ◽

Cited By ~ 19

Author(s):

M. W. Moncrieff ◽

D. W. K. So

Keyword(s):

Density Currents ◽

Hydrodynamical Theory

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XXV.—On the Hydrodynamical Theory of Seiches

Transactions of the Royal Society of Edinburgh ◽

10.1017/s0080456800035523 ◽

1906 ◽

Vol 41 (3) ◽

pp. 599-649 ◽

Cited By ~ 38

Author(s):

Chrystal

Keyword(s):

Surface Waves ◽

Direct Action ◽

Ocean Tides ◽

Lake Levels ◽

Surface Level ◽

Moderate Length ◽

Hydrodynamical Theory ◽

Recorded Observation

§ 1. The variations of the surface-level of lakes due to the direct action of wind and rain, and the smaller disturbances caused by surface waves, of small or moderate length, due to the action of the wind and the movement of boats and animals, must have been familiar phenomena at all times. The first accurately recorded observation, that lake-levels are subject to a rhythmic variation, similar in some respects to the ocean tides, seems to have been made at Geneva in 1730 by Fatio de Duillier, a well-known Swiss engineer. Owing to the peculiar configuration of the Geneva end of Lake Léman, these variations occasionally reach a magnitude of 5 or even 6 feet; and Duillier mentions that they were known in his time by the local name of “Seiches,” which has now been applied to rhythmic alterations of the level of lakes in general.

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A Hydrodynamical Theory of Piston Ring Lubrication

Physics ◽

10.1063/1.1745404 ◽

1936 ◽

Vol 7 (9) ◽

pp. 364-367 ◽

Cited By ~ 46

Author(s):

R. A. Castleman

Keyword(s):

Piston Ring ◽

Piston Ring Lubrication ◽

Hydrodynamical Theory

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The Hydrodynamical Theory of Surface Shear Viscosity

Progress in Surface and Membrane Science ◽

10.1016/b978-0-12-571807-3.50009-0 ◽

1973 ◽

pp. 151-181 ◽

Cited By ~ 4

Author(s):

F.C. GOODRICH

Keyword(s):

Shear Viscosity ◽

Surface Shear ◽

Hydrodynamical Theory ◽

Surface Shear Viscosity

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IX. On the application of harmonic analysis to the dynamical theory of the tides. — Part I. On laplace’s "oscillations of the first species” and the dynamics of ocean currents

Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character ◽

10.1098/rsta.1897.0009 ◽

1897 ◽

Vol 189 ◽

pp. 201-257 ◽

Cited By ~ 74

Keyword(s):

Ab Initio ◽

Harmonic Analysis ◽

Dynamical Theory ◽

Point Of View ◽

Ocean Currents ◽

Long Period ◽

Dynamical Treatment ◽

The Subject ◽

Hydrodynamical Theory

The earliest attempt to subject the Theory of the Tides to a rigorous dynamical treatment was given by Laplace in the first and fourth books of the ‘Mécanique Céleste.’ The subject has since been treated by Airy, Kelvin, Darwin, Lamb, and other writers, but with the exception of the extension of Laplace’s results to include the theory of the long-period tides, but little practical advance has been made with the subject, in spite of the enormous increase in the power of the mathematical resources at our disposal, and the problem has remained in very much the same condition as it was left by Laplace. This arises no doubt partly from the difficulties inherent to the subject, but partly from the form in which the theory was originally presented by Laplace in the ‘Mécanique Céleste,’ which has been described by Airy as “perhaps on the whole more obscure than any other part of the same extent in that work.” The obscurity complained of does not however seem to have been entirely removed by Laplace’s successors, and it was the fact that every presentment of the theory with which I was acquainted offered some points of difficulty, that in the first instance led me to take up the problem ab initio , partly with the purpose of allaying the doubts which had arisen in my own mind as to the validity of certain approximations employed by Laplace and adopted by his successors, and partly in the hope that I might be able to extend the results of Laplace to meet more fully the case presented by the circumstances actually existent in Nature. Up to the present I have been unable to free the problem to any extent from the limitations which have been imposed by previous writers, and consequently it would be futile to claim that the results I am now able to put forward materially advance our knowledge of the tides as they actually exist; but I venture to hope that these results, as applied to the oscillations of an ideal ocean, considerably simpler in character than the actual ocean, may prove of some interest from the point of view of pure hydrodynamical theory.

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