scholarly journals MODEL TESTS ON THE MOTION OF MOORED SHIPS PLACED ON LONG WAVES

2011 ◽  
Vol 1 (7) ◽  
pp. 40
Author(s):  
F.A. Kilner
Keyword(s):  
Strain Gauge ◽  
Wave Motion ◽  
Wave Length ◽  
Stationary Wave ◽  
Equation Of Motion ◽  
Wave Action ◽  
Stationary Waves ◽  
Elementary Analysis ◽  
Frictional Forces ◽  
Sway Motion

The equation of motion for a moored ship, subject to stationary wave action, is presented and discussed. The moorings are longitudinal, the ship is considered to be aligned to the direction of wave motion and positioned at a node, and the wave length is assumed long compared with the ship length. If the motion of the ship is assumed to be simple harmonic, and frictional forces between the ship and the water are neglected, an elementary analysis gives the required relation between the amplitudes of the ship's movement and of the water particle motion associated with the wave, A description is given of some tests carried out on model ships moored in a flume where stationary waves can be generated, and the amplitude and period can be varied independently. In these experiments, the amplitude of ship movement could be measured visually, or inferred from strain gauge readings, and the water motion was also observed. The results of these tests are compared with the simple theory. A table tilting harmonically is shown to be a mechanical analogy to stationary wave action on ships. The hydrodynamic mass for a ship moving in surge or sway motion is measured and is found to depend on the depth of water in which the ship is moored.

scholarly journals Localized stationary seismic waves predicted using a nonlinear gradient elasticity model

2021 ◽  
Author(s):  
Leo Dostal ◽  
Marten Hollm ◽  
Andrei V. Metrikine ◽  
Apostolos Tsouvalas ◽  
Karel N. van Dalen
Keyword(s):  
Homoclinic Orbit ◽  
Site Response ◽  
Gradient Elasticity ◽  
Stationary Wave ◽  
Equation Of Motion ◽  
Small Scale ◽  
Hyperbolic Model ◽  
Stationary Waves ◽  
Kink Wave ◽  
Strain Dependent

AbstractThis paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behavior is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear modulus. To this end, we derive a novel equation of motion for a nonlinear gradient elasticity model, where the higher-order gradient terms capture the effect of small-scale soil heterogeneity/micro-structure. We also present a novel finite-difference scheme to solve the nonlinear equation of motion in space and time. Simulations of the propagation of arbitrary initial pulses clearly reveal the influence of the nonlinearity: strain-dependent speed in general and, as a result, sharpening of the pulses. Stationary solutions of the equation of motion are obtained by introducing the moving reference frame together with the stationarity assumption. Periodic (with and without a descending trend) as well as localized stationary waves are found by analyzing the obtained ordinary differential equation in the phase portrait and integrating it along the different trajectories. The localized stationary wave is in fact a kink wave and is obtained by integration along a homoclinic orbit. In general, the closer the trajectory lies to a homoclinic orbit, the sharper the edges of the corresponding periodic stationary wave and the larger its period. Finally, we find that the kink wave is in fact not a true soliton as the original shapes of two colliding kink waves are not recovered after interaction. However, it may have high amplitude and reach the surface depending on the damping mechanisms (which have not been considered). Therefore, seismic site response analyses should not a priori exclude the presence of such localized stationary waves.

An experimental investigation of the nature and origin of microseisms at St. Louis, Missouri

1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez
Keyword(s):  
Wave Length ◽  
Vertical Axis ◽  
The Other ◽  
Wave Form ◽  
Stationary Waves ◽  
Retrograde Motion ◽  
Time Signals ◽  
Group Form ◽  
Triangular Network ◽  
The Waves

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.

scholarly journals Dynamical Processes Related to the Appearance of Quasi-Stationary Waves on the Subtropical Jet in the Midsummer Northern Hemisphere

2006 ◽  
Vol 19 (8) ◽  
pp. 1531-1544 ◽  
Author(s):  
Naoki Sato ◽  
Masaaki Takahashi
Keyword(s):  
Middle East ◽  
Northern Hemisphere ◽  
Wave Train ◽  
Stationary Wave ◽  
Stationary Waves ◽  
Statistical Features ◽  
Basic Field ◽  
Subtropical Jet ◽  
Anomaly Pattern ◽  
Highly Correlated

Abstract Statistical features of quasi-stationary planetary waves were examined on the subtropical jet in the midsummer Northern Hemisphere by using objectively analyzed data and satellite data. As a result, a quasi-stationary wave train that is highly correlated with the midsummer climate over Japan was identified. A clear phase dependency of the appearance of waves was also confirmed. An analysis of temporal evolution and wave activity flux revealed that the eastward propagation of the wave packet starts in the Middle East, passes over East Asia, and reaches North America. The anomaly pattern is strengthened through kinetic energy conversion near the entrance of the Asian jet over the Middle East. The interaction between the anomaly pattern and the basic field contributes to the appearance of the anomalous wavelike pattern. Although the wave train is correlated with the anomaly of convective activity over the western North Pacific and the Indian Ocean, it is implied that internal dynamics are important in determining the statistical features of the appearance of anomalous quasi-stationary waves on the subtropical jet.

scholarly journals Northern Hemisphere Stationary Waves in a Changing Climate

2019 ◽  
Vol 5 (4) ◽  
pp. 372-389 ◽  
Author(s):  
Robert C. J. Wills ◽  
Rachel H. White ◽  
Xavier J. Levine
Keyword(s):  
Climate Change ◽  
Atmospheric Circulation ◽  
Northern Hemisphere ◽  
Climate Models ◽  
Regional Climate ◽  
Stationary Wave ◽  
Future Research ◽  
Stationary Waves ◽  
The Pacific ◽  
Longitudinal Variations

Abstract Purpose of Review Stationary waves are planetary-scale longitudinal variations in the time-averaged atmospheric circulation. Here, we consider the projected response of Northern Hemisphere stationary waves to climate change in winter and summer. We discuss how the response varies across different metrics, identify robust responses, and review proposed mechanisms. Recent Findings Climate models project shifts in the prevailing wind patterns, with corresponding impacts on regional precipitation, temperature, and extreme events. Recent work has improved our understanding of the links between stationary waves and regional climate and identified robust stationary wave responses to climate change, which include an increased zonal lengthscale in winter, a poleward shift of the wintertime circulation over the Pacific, a weakening of monsoonal circulations, and an overall weakening of stationary wave circulations, particularly their divergent component and quasi-stationary disturbances. Summary Numerous factors influence Northern Hemisphere stationary waves, and mechanistic theories exist for only a few aspects of the stationary wave response to climate change. Idealized studies have proven useful for understanding the climate responses of particular atmospheric circulation features and should be a continued focus of future research.

scholarly journals Dynamics of Eddy-Driven Low-Frequency Dipole Modes. Part III: Meridional Displacement of Westerly Jet Anomalies during Two Phases of NAO

2007 ◽  
Vol 64 (9) ◽  
pp. 3232-3248 ◽  
Author(s):  
Dehai Luo ◽  
Tingting Gong ◽  
Yina Diao
Keyword(s):  
Theoretical Model ◽  
Storm Track ◽  
Low Frequency ◽  
Stationary Wave ◽  
Negative Phase ◽  
Stationary Waves ◽  
The North ◽  
Westerly Jet ◽  
Two Phases ◽  
The North Atlantic Oscillation

Abstract In this paper, the north–south variability of westerly jet anomalies during the two phases of the North Atlantic Oscillation (NAO) is examined in a theoretical model. It is found that the north–south variability of the zonal mean westerly anomaly results from the interaction between the eddy-driven anomalous stationary waves with a dipole meridional structure (NAO anomalies) and topographically induced climatological stationary waves with a monopole structure, which is dependent upon the phase of the NAO. The westerly jet anomaly tends to shift northward during the positive NAO phase but southward during the negative phase. Synoptic-scale eddies tend to maintain westerly jet anomalies through the excitation of NAO anomalies, but the climatological stationary wave and its position relative to the eddy-driven anomalous stationary wave appear to dominate the north–south shift of westerly jet anomalies. On the other hand, it is shown that when the climatological stationary wave ridge is located downstream of the eddy-driven anomalous stationary wave, the storm track modulated by the NAO pattern splits into two branches for the negative phase, in which the northern branch is generally stronger than the southern one. However, the southern one can be dominant as the relative position between anomalous and climatological stationary waves is within a moderate range. The storm track for the positive phase tends to drift northeastward when there is a phase difference between the NAO anomaly and climatological stationary wave ridge downstream. Thus, it appears that the relationship between the NAO jets and storm tracks can be clearly seen from the present theoretical model.

Floating Type Ocean Wave Power Station (Unique Work of Oscillating Platform)

2011 ◽  
Author(s):  
Takahiro Otsubo ◽  
Masayuki Orita ◽  
Tatsuya Kinoshita ◽  
Toshiaki Kanemoto ◽  
Kiyoshi Kokubu
Keyword(s):  
Wave Length ◽  
Hydraulic Turbine ◽  
Stationary Wave ◽  
Ocean Wave ◽  
Wave Power ◽  
Power Station ◽  
Floating Type ◽  
Oscillating Motion ◽  
Type Power ◽  
Dutch Roll

This paper presents the unique ocean wave power station, which is composed of the floating type platform with a pair of the floats lined up at the interval of one wave length and the counter-rotating type power unit submerged in the seawater at the middle position of the platform. Such profiles make the flow velocity through the turbines two times faster than that of the traditional OWC types, and make the turbine diameter large as possible because the rotational moment hardly acts on the platform. The previous paper verified that the station is effective to get the power from the ocean wave at the normally oscillating motion. Continuously, this paper discusses the effect of the wave length on the motion of the platform and present the flow conditions around Wells type hydraulic turbine in CFD. The platform in which the floats are at the symmetrical position to the anti-node oscillates normally irrespective of the stationary wave length. On the contrary, the platform with the floats the asymmetrically arranged or being at the progressive wave plays in the dutch-roll condition and does not get the fruitful power.

Investigating the Linear and Nonlinear Stationary Wave Response to Anomalous North American Snow Cover

2011 ◽  
Vol 68 (4) ◽  
pp. 904-917 ◽  
Author(s):  
Stefan Sobolowski ◽  
Gavin Gong ◽  
Mingfang Ting
Keyword(s):  
Snow Cover ◽  
North American ◽  
Land Surface ◽  
Large Scale ◽  
Wave Model ◽  
Stationary Wave ◽  
Response Analysis ◽  
Stationary Waves ◽  
Continental Scale ◽  
Wave Response

Abstract Continental-scale snow cover represents a broad thermal forcing on monthly-to-intraseasonal time scales, with the potential to modify local and remote atmospheric circulation. A previous GCM study reported robust transient-eddy responses to prescribed anomalous North American (NA) snow cover. The same set of experiments also indicated a robust upper-level stationary wave response during spring, but the nature of this response was not investigated until now. Here, the authors diagnose a deep, snow-induced, tropospheric cooling over NA and hypothesize that this may represent a pathway linking snow to the stationary wave response. A nonlinear stationary wave model is shown to reproduce the GCM stationary wave response to snow more accurately than a linear model, and results confirm that diabatic cooling is the primary driver of the stationary wave response. In particular, the total nonlinear effects due to cooling, and its interactions with transient eddies and orography, are shown to be essential for faithful reproduction of the GCM response. The nonlinear model results confirm that direct effects due to transients and orography are modest. However, with interactions between forcings included, the total effects due to these terms make important contributions to the total response. Analysis of observed NA snow cover and stationary waves is qualitatively similar to the patterns generated by the GCM and linear/nonlinear stationary wave models, indicating that the snow-induced signal is not simply a modeling artifact. The diagnosis and description of a snow–stationary wave relationship adds to the understanding of stationary waves and their forcing mechanisms, and this relationship suggests that large-scale changes in the land surface state may exert considerable influence on the atmosphere over hemispheric scales and thereby contribute to climate variability.

scholarly journals CHARACTERISTICS OF DIFFUSION AND AERATION DUE TO WAVE ACTION NEAR PERMEABLE BREAKWATERS

1988 ◽  
Vol 1 (21) ◽  
pp. 11
Author(s):  
Hitoshi Murakami ◽  
Yoshihiko Hosoi
Keyword(s):  
Diffusion Coefficient ◽  
Water Purification ◽  
Diffusion Coefficients ◽  
Wave Length ◽  
Wave Action ◽  
Reaeration Coefficient

This paper deals with the effect of wave action on the water purification near a permeable breakwater. When determining standards for water purification, three indexes are usually taken into account: the diffusion coefficient, the concentration reflection ratio and the reaeration coefficient. In our study, the values of the diffusion coefficients Kx near —12 2 the breakwater ranged from about 10 cm /sec to 7x10cm /sec. The effect of aeration caused by setting up a permeable breakwater was limited to within a distance of only one wave length at either side of the breakwater. As a result, values of the reaeration coefficients were then estimated to be in the order of 10 - 10 /sec.

scholarly journals QUASI-STATIONARY PLANETARY WAVES IN MID-LATITUDE STRATOSPHERE–MESOSPHERE IN WINTER 2011-2020

2021 ◽  
pp. 307-311
Author(s):  
Chenning Zhang ◽  
Oleksandr Evtushevsky ◽  
Gennadi Milinevsky
Keyword(s):  
Surface Pressure ◽  
Satellite Data ◽  
Geopotential Height ◽  
Stationary Wave ◽  
Planetary Waves ◽  
Stationary Waves ◽  
Aleutian Low ◽  
The North ◽  
Pressure Anomaly ◽  
Icelandic Low

The 10-year climatology (2011–2020) of quasi-stationary planetary waves in the mid-latitude stratosphere and mesosphere (40–50N, up to 90 km) has been analyzed. Longitude–altitude sections of geopotential height and ozone have been obtained using the Aura MLS satellite data. It is found that stationary wave 1 propagates into the mesosphere from the North American High and Icelandic Low, which are adjacent surface pressure anomalies in the structure of stationary wave 2. Unexpectedly, the strongest pressure anomaly in the Aleutian Low region does not contribute to the stationary wave 1 formation in the mesosphere. The vertical phase transformations of stationary waves in geopotential height and ozone show inconsistencies that should be studied separately.

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