Showing papers on "Rotation published in 1970"

Thermal instabilities in rapidly rotating systems

Abstract: Thermal instabilities of a contained fluid are investigated for a fairly general class of problems in which the dynamics are dominated by the effects of rotation. In systems of constant depth in the direction of the axis of rotation the instability develops when the buoyancy forces suffice to overcome the stabilizing effects of thermal conduction and of viscous dissipation in the Ekman boundary layers. Owing to the Taylor–Proudman theorem, a slight gradient in depth exerts a strongly stabilizing influence. The theory is applied to describe the instability of the ‘lower symmetric regime’ in the rotating annulus experiments at high rotation rates. An example of geophysical relevance is the instability of a self-gravitating, internally heated, rotating fluid sphere. The results of the perturbation theory for this problem agree reasonably well with the results of an extension of the analysis by Roberts (1968).

Inertial oscillations in a rotating fluid cylinder

Abstract: A study is described of the forced inertial oscillations appearing in an axially rotating completely filled circular cylinder with plane ends. Excitation is provided by causing the top end to rotate about an axis inclined slightly to the rotation axis. Experiments demonstrate the presence of numerous low mode resonances in a densely spaced range of ratios of net cylinder height to radius in close conformance with linear inviscid theory. Where geometry permits simple corner reflexion, characteristic surfaces are revealed which confirm in part the theoretical predictions concerning their scale and form.Detailed measurements are given of the amplitude at one point within the cylinder for the condition in which the disturbance frequency equals the rotation frequency. Amplitude column height spectra are compared with theoretical estimates, and the evolution of amplitude for the simplest mode of resonant oscillation is studied. A non-linear theory based on the integral energy of large amplitude oscillation is derived whose broad features are in fair quantitative and qualitative agreement with these observations.Some investigation is made of the phenomenon of resonant collapse, in which larger amplitude resonant oscillations, after persisting in an apparently laminar form, degenerate abruptly into a state of agitation and disorder from which they do not recover. It is found that the time for emergence of this collapse after the introduction of the forcing disturbance has a close correspondence with the theoretical period of one ‘evolutionary’ cycle of momentum exchange between the main motion and the secondary oscillation.

Differential rotation in stellar convection zones.

Abstract: The analysis of an earlier paper (Busse l970a) in which the differential rotation of the Sun was explained as the result of large scale convection in the solar convection zone is extended to include the detailed spatial dependence of the meridional circulation as well as of the differential rotation The thin shell approximation for a rotating spherical convection layer of a Boussinesq fluid is used The asymptotic representation of large order spherical harmonlcs by Hermite functions permits a simple integration of the equations for the meridional circulation and the differential rotation Explicit analytical solutions are given for the case of stressfree boundaries and numerical results are shown in the case of a rigid inner and a free outer boundary The case of stressfree boundaries is rather exceptional and the magnitude of the differential rotation is reduced for more general boundary conditions However, the differential rotation still exhibits the characteristic equatorial acceleration in the case of an inner rigid boundary (auth)

A Simple Method for the Solution of the Stellar Structure Equations Including Rotation and Tidal Forces

Abstract: In the following a method is presented for computing the internal structure of nonspherical stars assuming that the force per gram causing the deviation from spherical symmetry is conservative. The method has the advantage that in a normal (spherical) stellar structure code only slight changes have to be made in order to obtain nonspherical stellar models. The method can be applied as well to rotating stars as to stars distorted by tidal effects. Although it is similar to that of Faulkner et al. (1968) in the case of purely rotating stars, it is not necessary to use the division into two zones, where either slow rotation or negligible contribution to the gravitional potential is assumed.

The Effect of Blockage of All Six Semicircular Canal Ducts on Nystagmus Produced by Dynamic Linear Acceleration in the Cat

Abstract: Seven cats were given rotary tests about an earth-vertical axis and also about an earth-horizontal axis. They were tested with the sagittal head plane in the plane of rotation as well as with the horizontal head plane in the plane of rotation. Recordings of eye movements were made during the tests. Following surgical transection and blocking of all six semicircular ts canal ducthe cats were tested again. It was found postoperatively that horizontal and vertical nystagmus in response to angular acceleration about an earth-vertical axis were abolished. Nystagmus during constant velocity rotation about an earth-horizontal axis remained, however, although the slow phase eye velocity and frequency of the nystagmus were reduced. From these and other data it is suggested that although continuity of the semicircular canal ducts is necessary for the nystagmus in response to angular accelerations about a vertical axis, it is only contributory (and not necessary) for the nystagmus during constant velocity rotation a...

Differential rotation of the photospheric magnetic field.

Abstract: Photospheric magnetic field differential rotation using synoptic charts for autocorrelation technique

Interferometric measurement of angles.

Abstract: A new interferometric device for measuring small angles or rotations with high accuracy is described. This instrument works by counting fringes formed by the rotation of a flat-parallel plate of glass illuminated with a collimated beam from a gas laser. Some possible applications are given.

Cooperative Rotation of Spherical Molecules

Abstract: The rotational diffusion of molecules in the liquid and solid states can be studied by radiation scattering experiments. Both neutron and light scattering data are interpreted, conventionally, on the basis of rotation of single molecules, although in dense systems cooperative rotation is a possibility. It is pointed out that a comparison of incoherent neutron data and depolarized light data allows the cooperative nature of molecular rotational diffusion to be verified. The method is applied to the plastic crystal phase of cyclohexane, and it is shown that individual molecules rotate about 10 times as rapidly as the relaxation rate of the mean orientation of a group of molecules.

Differential rotation caused by anisotropic turbulent viscosity

Abstract: The law of rotation as well as the corresponding meridional circulations in the hydrogen convection zone (HCZ) are investigated by solving numerically the time independent Navier-Stokes equations. The HCZ is assumed to be a spherical layer of fluid with constant density and viscosity. It is assumed further that the viscosity is caused by unisotropic turbulent motions. The results show differential rotation together with circulations. The detailed behaviour depends on a parameters characterizing the nonisotropic friction and on the kinematic viscosityv. If the friction is larger in radial direction than in lateral directions (0 ⩽s 1) the equator rotates faster and the sense of the circulation is reversed. The differential rotation observed at the solar surface is obtained for the values = 1.2. For small values ofv the angular velocity is constant on cylindrical surfaces, for large values ofv it is constant on spherical surfaces. The solar law of rotation turns out to be very close to the first case.

Effects of Major Seismic Events on the Rotation of the Earth

Abstract: S-Y A spherical theory is advanced for perturbations of the Earth‘s rotation by major earthquakes and explosions. Explicit expressions are obtained for the dependence of the secular polar shift on the dimensions, depth, and location of the seismic event. Numerical results show that a single shallow earthquake of magnitude 8.5, occurring at a suitable latitude and with a favourable strike-azimuth, may suffice to maintain the Chandler wobble for about one year. Hence, it is deduced that earthquakes may at most 8ccouIlt for 30 per cent of the observed secular polar shift. 1. Introdoction The equations of rigid gyroscopic motion were given by Euler in 1758. On the basis of this theory, he suggested in 1765 that the Earth might undergo a free precession with period of A/(C-A) sideral days. Assuming this to be true, a spectator partaking in the Earth’s motion should observe periodic changes in latitude with a period of about 10 months. However, no such period could be found. Instead, Chandler established in 1891 the existence of a 428-days period in the spectrum of the latitude variation. The lengthening of the period was explained by Newcomb, in 1892, to be the result of the Earth’s elasticity. A theoretical veriiication was given by Love (1909), based on first-order theory of the figure of the Earth. This 14-month precessional motion of the instantaneous axis of rotation about the Earth’s axis of figure is known today as the Chandler Wobble. (Fig. 1.) Spectral analyses of latitude time series disclosed that the motion is damped with a ‘ Q ’ value between 30 and 40. The wobble must therefore be maintained by a certain source of energy. Munk & Macdonald (1960, p. 174) conclude that: ‘The statistical properties of the latitude time series are those associated with a damped oscillator excited at random. . . . Irregular variations of the atmosphere are the most likely cause of the wobble.’ Recently, however, observational evidence has been presented in support of the hypothesis that earthquakes may excite the wobble and produce the observed polar shift. To explain these arguments we shall recapitulate the theoretical background of the subject: The fundamental law of dynamics as experienced by earth-bound spectators is given by the Liouville equation (Munk & Macdonald 1960)

On the Determination of Barriers to Internal Rotation

Abstract: A method is presented for determining barriers to internal rotation directly from the spectrum of torsional energy levels without an a priori knowledge of either molecular geometry or the dynamics of the motion. The method is applied to the H2O2 and D2O2 molecules. It is also shown that the neglect of the variation of the effective inverse moment of inertia of threefold rotors can lead to an apparent V6 contribution to the potential function.

Structure of Jupiter - Chemical composition, contraction, and rotation

Abstract: Jupiter model construction from improved state equation, considering chemical composition, contraction and rotation

Axial flow pump

Abstract: An axial flow pump includes a housing supporting a tubular, electric motor driven pump body for rotation about an axis, and a plurality of impeller units detachably supported within the tubular pump body. The impeller units are constructed to provide a substantially unobstructed axial pumping passage through the pump body and are removable from the pump body without requiring disassembly of the pump body or the housing.

Fluid actuated clamp

Abstract: A bowed web of resiliently flexible material is deflected toward a straightened condition by pressure fluid and creates a clamping force with a toggle action to lock first and second parts against relative sliding and/or rotation

Inability to perceive the direction of rotation movement of line segments.

Abstract: A difference in speed of rotation, but not a difference in the direction of rotation alone, serves to make an array of line segments in a computer generated movie discernible from the background. The finding outlines some of the limitations of the human visual system.

An Experimental Study of Inertial Waves in a Closed Cone

Abstract: An experimental study of inertial waves in a closed cone is presented in which the inertial waves are excited by a slight periodic oscillation superimposed on the cone's basic rotation rate. The dynamic pressure field is measured along the cone's rotation axis; no standing modal structure is observed, confirming Greenspan's (1969) argument that the closed cone appears open to inertial oscillations and the inertial wave spectrum is continuous. Similar pressure measurements made in the frustum of a right circular cone show that removal of the singular apex of the cone leads to standing wave modes.

Global stability of spiral flow

Abstract: Energy and linear limits are calculated for the Poiseuille–Couette spiral motion between concentric cylinders which rotate rigidly and rotate and slide relative to one another. The addition of solid rotation can bring the linear limit down to the energy limit with coincidence achieved in the limit of infinitely fast rotation. If the differential rotation is also added, the solid rotation rate need be only finite to achieve near coincidence. Sufficient conditions for non-existence of sub-linear instability are derived. The basic spiral character of the instability is analysed and the results compared with the experiments of Ludwieg (1964).

Cylindrical tank of fluid oscillating about a state of steady rotation.

Abstract: : The study concerns a cylindrical tank, full of fluid, which is oscillating and rotating about its axis of symmetry. It is assumed that the amplitude of oscillation is small and the viscosity is low such that boundary layers exist. Analysis shows the unsteady boundary layer thickness on the top and bottom plates' thickness on the side walls. The interior unsteady flow shows source-like behavior at the corners. The steady flow field is caused by the steady component of the non-linear centrifugal forces coupled with an induced steady rotation of the interior. (Author)

Method and device for friction welding

Abstract: The method of friction welding is applicable to surfaces to be welded with any type of marginal boundary. Two workpieces to be welded together are arranged against each other at the surfaces to be welded and are heated to welding temperature by a relative oscillatory movement along such surfaces. The relative oscillatory movement is effected by way of relative rotatory movement with the workpieces remaining substantially parallel to each other. A device for carrying out the method comprises a workpiece holder driven by an eccentric body rotatable about an axis. A circular rotatory path is defined on the body and the eccentricity of this path is adjustable relatively to said axis, the holder being movable at least two-dimensionally in a plane corresponding to the orientation of the surface to be welded. The holder is guided on the path of progression of the eccentric body so that, upon rotation of that body, all parts of the holder perform rotatory movements of equal size and circular shape with a radius equal to the adjusted eccentricity of the eccentric body.

Golf practice device

Abstract: A plate is connected at its bottom by a hinge to a vertical support. Brackets at the top of the plate can be connected to the support in various positions to change the angle of inclination of the plate. An arm is rotatably connected to the plate for rotation about an axis normal to the plate. The frictional drag of the rotation of the arm may be adjusted. On the distal end of the arm is a simulated golf club handle. Immediately above the axis of rotation of the arm is an adjustably positioned headrest.