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.

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 Planetary wave activity in the polar lower stratosphere

2010 ◽  
Vol 10 (2) ◽  
pp. 707-718 ◽  
Author(s):  
S. P. Alexander ◽  
M. G. Shepherd
Keyword(s):  
Planetary Wave ◽  
Travelling Waves ◽  
Stationary Wave ◽  
Wave Activity ◽  
The Arctic ◽  
Small Scale ◽  
Stationary Waves ◽  
Significant Activity ◽  
Zonal Wavenumber ◽  
The Times

Abstract. Temperature data from the COSMIC GPS-RO satellite constellation are used to study the distribution and variability of planetary wave activity in the low to mid- stratosphere (15–40 km) of the Arctic and Antarctic from September 2006 until March 2009. Stationary waves are separated from travelling waves and their amplitudes, periods and small-scale vertical distribution then examined. COSMIC observed short lived (less than two weeks and less than 5 km vertically) but large enhancements in planetary wave amplitudes occurring regularly throughout all winters in both hemispheres. In contrast to recent Arctic winters, eastward wave activity during 2008–2009 was significantly reduced during the early part of the winter and immediately prior to the major SSW. The eastward waves which did exist had similar periods to the two preceding winters (~16–20 days). A westward wave with zonal wavenumber two, with distinct peaks at 22 km and 35 km and period around 16–24 days, as well as a stationary wave two were associated with the 2009 major SSW. In the Southern Hemisphere, the height structure of planetary wave amplitudes also exhibited fluctuations on short time and vertical scales superimposed upon the broader seasonal cycle. Significant inter-annual variability in planetary wave amplitude and period are noticed, with the times of cessation of significant activity also varying.

scholarly journals Experimental and analytical study of seismic site response of discontinuous permafrost

2016 ◽  
Vol 53 (9) ◽  
pp. 1363-1375 ◽  
Author(s):  
Behrang Dadfar ◽  
M. Hesham El Naggar ◽  
Miroslav Nastev
Keyword(s):  
Shear Wave ◽  
Site Response ◽  
Free Field ◽  
Frozen Soil ◽  
Shaking Table ◽  
Experimental Program ◽  
Small Scale ◽  
Seismic Site Response ◽  
Discontinuous Permafrost ◽  
Spectral Accelerations

Seismic site response of discontinuous permafrost is discussed. The presence of frozen ground in soil deposits can significantly affect their dynamic response due to stiffer conditions characterized by higher shear-wave velocities compared to unfrozen soils. Both experimental and numerical investigations were conducted to examine the problem. The experimental program included a series of 1g shaking table tests on small-scale models. Nonlinear numerical analyses were performed employing FLAC software. The numerical model was verified using the obtained experimental results. Parametric simulations were then conducted using the verified model to study variations of the free-field spectral accelerations (on top of the frozen and unfrozen soil blocks) with the scheme of frozen–unfrozen soil, and to determine the key parameters and their effects on seismic site response. Results show that spectral accelerations were generally higher in frozen soils than in unfrozen ones. It was found that the shear-wave velocity of the frozen soil as well as the assumed geometry of the blocks and their spacing have a significant impact on the site response.

Atmospheric general circulation and waves simulated by a Venus AORI GCM with topographical and radiative forcings

2021 ◽  
Author(s):  
Masaru Yamamoto ◽  
Takumi Hirose ◽  
Kohei Ikeda ◽  
Masaaki Takahashi
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Circulation Model ◽  
Stationary Wave ◽  
Static Stability ◽  
Small Scale ◽  
Mean Flow ◽  
Short Period ◽  
Low Latitudes ◽  
Thermal Tides

<p>General circulation and waves are investigated using a T63 Venus general circulation model (GCM) with solar and thermal radiative transfer in the presence of high-resolution surface topography. This model has been developed by Ikeda (2011) at the Atmosphere and Ocean Research Institute (AORI), the University of Tokyo, and was used in Yamamoto et al. (2019, 2021). In the wind and static stability structures similar to the observed ones, the waves are investigated. Around the cloud-heating maximum (~65 km), the simulated thermal tides accelerate an equatorial superrotational flow with a speed of ~90 m/s<sup></sup>with rates of 0.2–0.5 m/s/(Earth day) via both horizontal and vertical momentum fluxes at low latitudes. Over the high mountains at low latitudes, the vertical wind variance at the cloud top is produced by topographically-fixed, short-period eddies, indicating penetrative plumes and gravity waves. In the solar-fixed coordinate system, the variances (i.e., the activity of waves other than thermal tides) of flow are relatively higher on the night-side than on the dayside at the cloud top. The local-time variation of the vertical eddy momentum flux is produced by both thermal tides and solar-related, small-scale gravity waves. Around the cloud bottom, the 9-day super-rotation of the zonal mean flow has a weak equatorial maximum and the 7.5-day Kelvin-like wave has an equatorial jet-like wind of 60-70 m/s. Because we discussed the thermal tide and topographically stationary wave in Yamamoto et al. (2021), we focus on the short-period eddies in the presentation.</p>

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.

The 1983 Liege Earthquake: Damage Distribution and Site Effects

1990 ◽  
Vol 6 (4) ◽  
pp. 713-737 ◽  
Author(s):  
D. Jongmans ◽  
M. Campillo
Keyword(s):  
Site Effects ◽  
Large Scale ◽  
Site Response ◽  
Dominant Frequency ◽  
Small Scale ◽  
Eastern United States ◽  
Frequency Range ◽  
Damage Distribution ◽  
Damage Data ◽  
The City

On November 8, 1983, a moderate magnitude (Ml=4.9) earthquake struck Liege (Belgium). A damage study has shown that site effects at different scales have played an important role in amplifying ground motion. On a large scale, the damage distribution has been determined by the presence of a large Carboniferous syncline beneath the city as shown by 2D numerical modeling. On a small scale, the main damage concentrations can be correlated with local superficial deposits which have amplified ground motions in the frequency range of buildings. A geophysical survey was carried out to measure the shear wave velocity of the different formations. Site response computations were made at numerous sites in order to estimate the possible amplification and to compare the results with the damage. It was shown that the spectral amplifications computed in the dominant frequency range of the buildings are consistent with the damage data. In very affected areas, 1D amplifications of 4 to 6 were obtained and in some cases 2D effects may have occurred. The Liege earthquake, taking place in the intraplate region of Northwestern Europe, presents a significant interest to other similar areas as the eastern United States.

Enhanced dissipation for quasi-geostrophic motion over small-scale topography

2000 ◽  
Vol 407 ◽  
pp. 105-122 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Additional Term ◽  
Equation Of Motion ◽  
Small Scale ◽  
Two Dimensional ◽  
Turbulent Dissipation ◽  
Dissipative Term ◽  
History Of ◽  
Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

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.

scholarly journals Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1935 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Krzysztof Kamil Żur
Keyword(s):  
Material Properties ◽  
Gradient Elasticity ◽  
Small Scale ◽  
Stability Equation ◽  
Strain Gradients ◽  
Size Dependent ◽  
Different Types ◽  
Dependent Property ◽  
The Stability ◽  
Transverse Deflection

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant.

Sign in / Sign up

Export Citation Format

Share Document