Seismic seiches in Norway and England during the Assam earthquake of August 15, 1950*

1955 ◽  
Vol 45 (2) ◽  
pp. 93-113
Author(s):  
Anders Kvale
Keyword(s):  
Standing Waves ◽  
Vertical Direction ◽  
Maximum Amplitude ◽  
Long Waves ◽  
Water Reservoirs ◽  
Lisbon Earthquake ◽  
Seismological Observatory ◽  
Progressive Waves ◽  
The Waves ◽  
East West

Abstract During the Assam earthquake of August 15, 1950, unusual waves were observed in at least 37 localities in fjords and lakes in Norway. Reports from 29 of these are discussed in this paper. In most places the waves were standing waves, with periods of 1 to 3 minutes and amplitudes of 5 to 100 cm. and began when the acceleration at the seismological observatory in Bergen surpassed 20 milligals in the east-west direction and 40 milligals in the vertical direction. The movements generally ceased when the acceleration decreased to below 10 milligals. The main periods of the long waves declined during this period from about 30 to 15 seconds, but the seismograms also indicate longer periods, of about 1 to 3 minutes, which may have some connection with the seiches. The calculated periods for the basins where waves were observed are, assuming one node, in most places between 1 and 3 minutes. In England, standing oscillations were recorded in water reservoirs at Margate, Chichester, and Portsmouth during the earthquake. The periods cannot be determined from the records, but the calculated periods vary from 15 to 25 seconds, which corresponds fairly closely with the 22 seconds given by Kew Observatory as the period of the long waves of the earthquake. The maximum amplitude in the reservoirs was 2 inches. Seiches in Norway during the Lisbon earthquake of November 1, 1755, and progressive waves during the Kansu earthquake of December 16, 1920, are briefly discussed.

scholarly journals Study on dynamic characteristics of leaf spring system in vibration screen

2021 ◽  
pp. 146134842110229
Author(s):  
Jiacheng Zhou ◽  
Chao Hu ◽  
Ziqiu Wang ◽  
Zhengfa Ren ◽  
Xiaoyu Wang ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Vertical Direction ◽  
Maximum Amplitude ◽  
Exciting Force ◽  
Mode Shapes ◽  
Leaf Spring ◽  
Amplification Factors ◽  
Simulation And Experiment ◽  
Exciting Forces ◽  
Spring System

By studying dynamic characteristics of the leaf spring system, a new elastic component is designed to reduce the working load and to a certain extent to ensure the linearity as well as increase the amplitude in the vertical and horizontal directions in vibration screen. The modal parameters, amplitudes, and amplification factors of the leaf spring system are studied by simulation and experiment. The modal results show that the leaf spring system vibrates in horizontal and vertical directions in first and second mode shapes, respectively. It is conducive to loosening and moving the particles on the vibration screen. In addition, it is found that the maximum amplitude and amplification factor in the horizontal direction appear at 300 r/min (5 Hz) while those in the vertical direction appear at 480 r/min (8 Hz), which are higher than those in the disc spring system. Moreover, the amplitude of the leaf spring system increases proportionally with the increase of exciting force while the amplification factors are basically the same under different exciting forces, indicating the good linearity of the leaf spring system. Furthermore, the minimum exciting force occurs in the leaf spring system under the same amplitude by comparing the exciting force among different elastic components. The above works can provide guidance for the industrial production in vibration screen.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

Effect of Spatial Variation of a Wave Field on the Resulting Ripple Characteristics and Comparison to Present Ripple Predictors

2009 ◽  
Author(s):  
Blake J. Landry ◽  
Yovanni A. Catan˜o-Lopera ◽  
Matthew J. Hancock ◽  
Chiang C. Mei ◽  
Marcelo H. Garci´a
Keyword(s):  
Spatial Variation ◽  
Wave Field ◽  
Test Section ◽  
Laboratory Experiments ◽  
Laboratory Data ◽  
Standing Waves ◽  
Sand Ripple ◽  
Wave Measurements ◽  
Progressive Waves ◽  
Sediment Test

Laboratory experiments analyzed herein focus on the validity of ripple predictors under spatially variable wave envelopes. Present-day ripple predictors commonly derived from laboratory data (for smaller wave periods of about 1 to 4 s) within which only small regions of the facilities were used to observe and measure the sand ripple geometric characteristics of the nearly progressive waves measured overhead. When extended to large sediment test sections, our results show that the predictors are still valid along the tank under wave conditions which have significant wave envelope spatial variation (e.g., standing waves), provided that ripple predictors use the wave measurements directly above the respective locations within the computations. Results indicate that even under the case of mild reflection, noticeable variation in ripple characteristics can be seen along the sediment test section; thus, compels the necessity of measuring the wave field along the entire sediment section to achieve accurate results.

scholarly journals Reflection of nonlinear deep-water waves incident onto a wedge of arbitrary angle

1990 ◽  
Vol 32 (1) ◽  
pp. 61-96 ◽  
Author(s):  
T. R. Marchant ◽  
A. J. Roberts
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Wave Reflection ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Arbitrary Angle ◽  
Weakly Nonlinear ◽  
Progressive Waves ◽  
The Waves ◽  
Wave Properties

AbstractWave reflection by a wedge in deep water is examined, where the wedge can represent a breakwater of finite length or the bow of a ship heading directly into the waves. In addition, the form of the solution allows the results to apply to ships heading at an angle into the waves. We consider a deep-water wavetrain approaching the wedge head on from infinity and being reflected. Far from the wedge there is a field of progressive waves (the incident wavetrain) while close to the wedge there is a short-crested wavefield (the incident and reflected wavetrains). A weakly-nonlinear slowly-varying averaged Lagrangian theory is used to describe the problem (see Whitham [16]) as the theory includes the nonlinear interaction between the incident and reflected wavetrains. This modelling of a short-crested wavefield allows the nonlinear wavefield to be found for broad wedges, as opposed to previous theories which are applicable to thin wedges only.It is shown that the governing partial differential equations are hyperbolic and that the solution comprises two regions, within which the wave properties are constant separated by a wave jump. Given the wedge angle and the incident wavefield, the jump angle and the wave steepness and wavenumber of the short-crested wave-field behind the wave jump can be determined. Two solution branches are found to exist: one corresponds to regular reflection, while for small amplitudes the other is similar to Mach-reflection and so it is called near Mach-reflection. Results are presented describing both solution branches and the transition between them.

scholarly journals On the theory of long waves and bores

1914 ◽  
Vol 90 (619) ◽  
pp. 324-328 ◽  
Keyword(s):  
Steady Motion ◽  
Vertical Direction ◽  
Two Dimensions ◽  
Long Waves ◽  
Horizontal Velocity

In the theory of long waves in two dimensions, which we may suppose to be reduced to a "steady" motion, it is assumed that the length is so great in proportion to the depth of the water that the velocity in a vertical direction can be neglected, and that the horizontal velocity is uniform across each section of the canal. This, it should be observed, is perfectly distinct from any supposition as to the height of the wave. If l be the undisturbed depth, and h the elevation of the water at any point of the wave, u 0 , u the velocities corresponding to l , l + h respectively, we have, as the equation of continuity, u = lu 0 / l + h . (1) By the the principles of hydrodyamics, the increase of pressure due to retardation will be ½ ρ ( u 0 2 - u 2 ) = ρu 0 2 /2. 2 lh + h 2 /( l + h ) 2 . (2)

Broadband Random Phase Diffuser for Ultrasonic Imaging

1979 ◽  
Vol 1 (4) ◽  
pp. 325-332
Author(s):  
Gerard A. Alphonse ◽  
David Vilkomerso
Keyword(s):  
Solid Angle ◽  
Random Phase ◽  
Ultrasonic Imaging ◽  
Standing Waves ◽  
Acoustic Imaging ◽  
Point Sources ◽  
Phase Plate ◽  
Reflected Waves ◽  
Large Aperture ◽  
The Waves

In reflective imaging, waves must be scattered by the object over a broad solid angle so that some of the reflected waves impinge upon the collecting aperture. Surfaces such as biological specimens under study in acoustic imaging are considered smooth at the wavelengths used (e.g., 1 mm) and therefore act as specular reflectors. In order to obtain reflection over a broad spatial range, large aperture, sector or compound scanning are used. In certain types of systems, diffuse insonification is sometimes used by imaging a raster of random phase points onto the surface. However interference between the waves from these point sources produces random fringes or “speckle-like” patterns overlaying the image. In optics these fringes have been reduced by rotating the diffuser. A similar approach has been taken here. This paper describes a simple random phase plate having two levels, 0° and 180 phase that can, by rotation, change the relative phases of the diffuse insonification points so as to reduce the speckle-like effect in the image. The temporal bandwidth of the random phase plate is narrow because of standing waves in it. To reduce standing waves the diffuser is intimately coupled to a wedged transducer. This combination is used to obtain diffuse insonification with broad spatial and temporal bandwidth.

On the observability of finite-depth short-crested water waves

1996 ◽  
Vol 322 ◽  
pp. 1-19 ◽  
Author(s):  
M. Ioualalen ◽  
A. J. Roberts ◽  
C. Kharif
Keyword(s):  
Standing Wave ◽  
Water Waves ◽  
Numerical Study ◽  
Standing Waves ◽  
Finite Depth ◽  
Two Dimensional ◽  
Wave Fields ◽  
Progressive Waves ◽  
Wave Limit ◽  
Narrow Bands

A numerical study of the superharmonic instabilities of short-crested waves on water of finite depth is performed in order to measure their time scales. It is shown that these superharmonic instabilities can be significant-unlike the deep-water case-in parts of the parameter regime. New resonances associated with the standing wave limit are studied closely. These instabilities ‘contaminate’ most of the parameter space, excluding that near two-dimensional progressive waves; however, they are significant only near the standing wave limit. The main result is that very narrow bands of both short-crested waves ‘close’ to two-dimensional standing waves, and of well developed short-crested waves, perturbed by superharmonic instabilities, are unstable for depths shallower than approximately a non-dimensional depth d= 1; the study is performed down to depth d= 0.5 beyond which the computations do not converge sufficiently. As a corollary, the present study predicts that these very narrow sub-domains of short-crested wave fields will not be observable, although most of the short-crested wave fields will be.

scholarly journals The pressure of a degenerate electron gas and related problems

1935 ◽  
Vol 152 (876) ◽  
pp. 253-272 ◽  
Author(s):  
Arthur Stanley Eddington
Keyword(s):  
Lorentz Transformation ◽  
Standing Waves ◽  
Relativity Theory ◽  
Rest Energy ◽  
Relativistic Formula ◽  
Slow Moving ◽  
Progressive Waves ◽  
Cell Divison ◽  
Dense Stars ◽  
Degenerate Electron Gas

1- The "ordinary" formula for the minimum electron pressure P corresponding to an electron density σ is of form P = Kσ. It has been generally accepted that this is a non-relativistic approximation, applying only to slow-moving electrons; and a "relativistic" formula has been given, intended to take account of change of mass with velocity. In a recent paper I have contended that the "ordinary" formula is the exact relativistic solution of the problem, and that the "relativistic" formula rests on a misconception. Since a decision on this point has far-reaching consequences in the theory of dense stars, and, moreover, has a fundamental bearing on the union of quantum theory with relativity theory, it has seemed desirable to supplement my earlier paper. I think the earlier paper makes it clear that whether the "relativistic" formula is right or wrong, existing proofs of it cannot be accepted. Briefly, the fallacy lies in the fact that the cell-divison of phase space is obtained by standing waves , but these are assigned an energy which has been derived for progressive waves . If this is not simply a mistake, it is a step which requires careful justification; and up to the present no one seems to have given any reason why one should assume that the energy or hamiltonian of standing waves is the same as that of pro-gressive waves. We may recall that the energy of plane progressive waves is easily calculated, because by a Lorentz transformation they are converted into waves advancing along the time-axis, and the energy is then the rest-energy of the particle; if the Lorentz transformation is applied to standing waves no such simplification results, and the reduction of the particle to rest involves an involves an altogether different type of transformation.

Propagation of long waves due to atmospheric disturbances on a rotating sea

1956 ◽  
Vol 233 (1195) ◽  
pp. 556-569 ◽  
Keyword(s):  
Steady State ◽  
Long Waves ◽  
Pressure Gradients ◽  
Constant Amplitude ◽  
Rotating System ◽  
Dispersive Waves ◽  
Atmospheric Disturbances ◽  
The Waves ◽  
Steady State Amplitude ◽  
Maximum Group

Long waves in shallow water in a non-rotating system are not dispersive but in a rotating system they are. This paper investigates the generation and propagation of these dispersive waves in an infinite sea. The mode of generation is by air-pressure gradients or wind stresses applied to the surface. Bottom friction is neglected. The surface elevation due to a stationary force of constant amplitude suddenly applied and maintained at t = 0 over one-half of an infinite sea is shown to approach, through a series of oscillations approximating more or less to an inertia period, a steady-state amplitude decreasing with distance from the generating area, The longitudinal and transverse velocities are also given. The time elapsed from the initial disturbance at a point to the first maximum of elevation decreases with the distance of the point from the edge of the generating area. A generating area whose edge moves forward with the maximum group velocity of the waves is shown to lead to an elevation of ever-increasing height. The effect of a barrier placed at right angles to the direction of propagation is also briefly considered.

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