Long-period Waves Research Articles

Experimental and modelling study on the response of mooring container ships in port under medium to long period waves

For understanding the influence of medium to long period waves on the dynamic response of ships, the hydrodynamic analysis of three typical moored container ships under wave interaction is carried out based on potential flow theory. The calculated and experimental results comparison shows that the numerical calculation is more suitable for simulation of long-period wave, as the dynamic response of ship is larger, but more accurate. For the larger ship, the peak response period of the mooring system usually reaches 100 s because the mooring stiffness is relatively small. With extended wave period, the ship motion response increases almost linearly. The symmetrical mooring arrangement and the similar mooring stiffness can effectively reduce the inhomogeneity of mooring forces. In addition, the ship motion and mooring force response can reach a minimum value at a special angle between ship and wave.

Leaky Slope Waves and Sea Level: Unusual Consequences of the Beta Effect along Western Boundaries with Bottom Topography and Dissipation

ABSTRACTCoastal trapped waves (CTWs) carry the ocean’s response to changes in forcing along boundaries and are important mechanisms in the context of coastal sea level and the meridional overturning circulation. Motivated by the western boundary response to high-latitude and open-ocean variability, we use a linear, barotropic model to investigate how the latitude dependence of the Coriolis parameter (β effect), bottom topography, and bottom friction modify the evolution of western boundary CTWs and sea level. For annual and longer period waves, the boundary response is characterized by modified shelf waves and a new class of leaky slope waves that propagate alongshore, typically at an order slower than shelf waves, and radiate short Rossby waves into the interior. Energy is not only transmitted equatorward along the slope, but also eastward into the interior, leading to the dissipation of energy locally and offshore. The β effect and friction result in shelf and slope waves that decay alongshore in the direction of the equator, decreasing the extent to which high-latitude variability affects lower latitudes and increasing the penetration of open-ocean variability onto the shelf—narrower continental shelves and larger friction coefficients increase this penetration. The theory is compared with observations of sea level along the North American east coast and qualitatively reproduces the southward displacement and amplitude attenuation of coastal sea level relative to the open ocean. The implications are that the β effect, topography, and friction are important in determining where along the coast sea level variability hot spots occur.

Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrödinger equations

We study the dynamics and energy exchanges between a linear oscillator and a nonlinear interaction state for the one dimensional, quintic nonlinear Schrodinger equation. Grebert and Thomann [ 9 ] proved that there exist solutions with initial data built on four Fourier modes, that confirm the conservative exchange of wave energy. Captured multi resonance in multiple Fourier modes, we simulate a similar energy exchange in long-period waves.

Numerical investigation on tsunami wave mitigation on forest sloping beach

An explicit one-dimensional model based on the shallow water equations (SWEs) was established in this work to simulate tsunami wave propagation on a vegetated beach. This model adopted the finite-volume method (FVM) for maintaining the mass balance of these equations. The resistance force caused by vegetation was taken into account as a source term in the momentum equation. The Harten–Lax–van Leer (HLL) approximate Riemann solver was applied to evaluate the interface fluxes for tracing the wet/dry transition boundary. This proposed model was used to simulate solitary wave run-up and long-periodic wave propagation on a sloping beach. The calibration process suitably compared the calculated results with the measured data. The tsunami waves were also simulated to discuss the water depth, tsunami force, as well as the current speed in absence of and in presence of forest domain. The results indicated that forest growth at the beach reduced wave energy loss caused by tsunamis. A series of sensitivity analyses were conducted with respect to variable parameters (such as vegetation densities, wave heights, wave periods, bed resistance, and beach slopes) to identify important influences on mitigating tsunami damage on coastal forest beach.

STATISTICALLY SIGNIFICANT ESTIMATES OF INFLUENCE OF SOLAR ACTIVITY ON PLANETARY WAVES IN THE MIDDLE ATMOSPHERE OF THE NORTHERN HEMISPHERE AS DERIVED FROM MUAM MODEL DATA

Numerical simulation has been used to examine the effect of changes in solar activity (SA) in the thermosphere on amplitudes of long-period planetary waves (PW) for the winter period in the Northern Hemisphere. The model of the middle and upper atmosphere (MUAM) is used. It allows simulations of general atmospheric circulation at altitudes 0–300 km. In order to reproduce SA changes, different values of the solar radio flux at a wavelength of 10.7 cm at an altitude of more than 100 km are set in the MUAM radiation block. To take into account the effect of charged particles in the ionosphere on the neutral gas dynamics, ionospheric conductivities for different SA levels are included in MUAM. To improve the statistical reliability of the results, two ensembles of model simulations consisting of 16 runs corresponding to the minimum and maximum SA have been obtained. The statistical confidence of average differences in PW amplitudes between high and low SA has been calculated. The results are shown to be reliable in almost the entire altitude range 0–300 km. Results of the simulations have shown for the first time that statistically significant differences in amplitudes of long-period PWs can reach 10–15 % in the middle atmosphere of the Northern Hemisphere, depending on the zonal wave number. At the same time, reflection of PWs at altitudes of lower thermosphere has a significant effect on the PW structure in the middle atmosphere.

СТАТИСТИЧЕСКИ ЗНАЧИМЫЕ ОЦЕНКИ ВЛИЯНИЯ СОЛНЕЧНОЙ АКТИВНОСТИ НА ПЛАНЕТАРНЫЕ ВОЛНЫ В СРЕДНЕЙ АТМОСФЕРЕ СЕВЕРНОГО ПОЛУШАРИЯ ПО ДАННЫМ МОДЕЛИ МСВА

Numerical simulation has been used to examine the effect of changes in solar activity (SA) in the thermosphere on amplitudes of long-period planetary waves (PW) for the winter period in the Northern Hemisphere. The model of the middle and upper atmosphere (MUAM) is used. It allows simulations of general atmospheric circulation at altitudes 0–300 km. In order to reproduce SA changes, different values of the solar radio flux at a wavelength of 10.7 cm at an altitude of more than 100 km are set in the MUAM radiation block. To take into account the effect of charged particles in the ionosphere on the neutral gas dynamics, ionospheric conductivities for different SA levels are included in MUAM. To improve the statistical reliability of the results, two ensembles of model simulations consisting of 16 runs corresponding to the minimum and maximum SA have been obtained. The statistical confidence of average differences in PW amplitudes between high and low SA has been calculated. The results are shown to be reliable in almost the entire altitude range 0–300 km. Results of the simulations have shown for the first time that statistically significant differences in amplitudes of long-period PWs can reach 10–15 % in the middle atmosphere of the Northern Hemisphere, depending on the zonal wave number. At the same time, reflection of PWs at altitudes of lower thermosphere has a significant effect on the PW structure in the middle atmosphere.

Quantizing soliton-like phonon pulse and optical branch of lattice vibration at crack tip excited by crack propagation as shock waves

In the previous paper (Kobayashi, 2019) based on the proposed micro-crack evolution equation, a solitary pulse wave radiated by crack propagation as the shock wave was analyzed and the solitary character of the solitary pulse wave was examined due to its energy and acceleration. Subsequently, in this viewpoint, the solitary pulse wave was concluded to be a soliton. In this paper, the lattice vibration at the crack tip excited by the crack propagation as a shock wave is examined by considering the shock wave velocity at the crack tip, and then the lattice vibration excited at the crack tip is concluded to be optical branch (mode). Therefore, optical and/or electrical phenomena may be exited at the crack tip due to the crack propagation as shock waves. Based on the optical branch, the mechanism, that causes discontinuity, singularity, the non-locality and also the entanglement in the fracture progress process, is discussed. The correlation of parameters introduced in the previous paper with number and energy of phonons is examined in the viewpoint of quantizing a soliton-like phonon pulse. As a result, it is clarified that the amplitude of the soliton-like phonon pulse cannot be determined arbitrarily and, hence, is a discrete value. Here, the proposed soliton-like phonon pulse may be recognized as a topological soliton of the strain induced by a kink of the displacement occurred by explicit or spontaneous symmetry breaking in the (1+1) dimensional space due to the crack propagation. Therefore, it is suggested that fracture induces phase transformation. The long-period pulse waves that were observed in the seismograms of the 2016 Kumamoto Earthquake and the 2018 Hokkaido Eastern Iburi Earthquake at the neighborhood of the seismic centers are examined in detail in the viewpoint of the proposed quantization of a soliton-like phonon pulse. Then the long-period pulse waves observed in earthquakes are simulated using the value of the proposed parameter λIc determined by the earthquake energy calculated by its magnitude, and its fault area is estimated using the relation between the fracture area and the fracture energy derived in the previous paper (Kobayashi, 2017b). In this paper, the author suggests some examples in which micro-scale properties such as quantum character visibly reflect in macro-scale phenomena.

An experimental study on hydrodynamic performance of a box-floating breakwater in different terrains

An experimental investigation on the hydrodynamic performance of a box-floating breakwater in different terrains is performed in a 2D wave flume under regular wave actions and irregular wave actions, respectively. The wave transmission coefficients, motion responses and mooring forces are focused to validate the hydrodynamic performance of the box-floating breakwater. The performance of the box-floating breakwater in flat terrain is also experimentally investigated for comparison. The influences of the terrain width and quantity on the hydrodynamic behaviors of the box-floating breakwater are discussed and analyzed. The results indicate that the box-floating breakwater in different terrains has a better wave attenuating ability than the box-floating breakwater in flat terrain due to wave energy loss caused by the interaction between the breakwater and terrain. However, the width of terrain has a limited effect on the hydrodynamic performance of the floating breakwater. For double terrains, the wave attenuation performance of the box-type floating breakwater increases with the decrease of the spacing between double terrains, especially for long-period waves. It is also found that terrain has significant influences on the roll and heave motions, while terrain hardly affects the sway motions. In addition, terrain plays an important role in the mooring forces, while the width and quantity of terrain weakly affect the mooring forces of box-floating breakwater. To investigate the hydrodynamic performance of rectangular floating breakwater in different terrains systematically, Smoothed Particle Hydrodynamics (SPH) methods is used. It can be concluded that the results of SPH show a good agreement with the experimental results.

Study on boundary layer development and bottom shear stress beneath a tsunami

ABSTRACTThis paper presents a detailed investigation on unsteady effects in bottom boundary layer beneath a tsunami. In numerical simulation of tsunami, bottom shear stress has commonly been evaluated by using steady flow friction laws such as Manning equation, simply assuming that long-period wave motion satisfies quasi-steady flow conditions. However, the present study found that the behavior of tsunami-induced bottom boundary layer has an unsteady characteristics and acts similar to that induced by wind-generated waves even under long-period wave motion. As a result, bottom shear stress under tsunami is much larger than the estimation using steady friction coefficient due to a steep velocity gradient in the bottom boundary layer. Surprisingly, the steady flow friction law is not valid in almost the entire computational domain, from the source area to shallow region. This result highly coincides with the field measurement data obtained by Lacy group during the 2010 Chilean Tsunami at the Monterey Bay mouth in U.S. A correction coefficient is proposed to take into account unsteady effects in the conventional estimation method using a steady friction factor; this approach is validated by comparing with numerical simulation results using k-ω turbulence model.

Theory of standing spin waves in a finite-size chiral spin soliton lattice

We present a theory of standing spin wave (SSW) in a monoaxial chiral helimagnet. Motivated by experimental findings on the magnetic field-dependence of the resonance frequency in thin films of Cr${}$Nb$_{3} $S${}_{6}$[Goncalves et al., Phys. Rev. B95, 104415 (2017)], we examine the SSW over a chiral soliton lattice (CSL) excited by an ac magnetic field applied parallel and perpendicular to the chiral axis. For this purpose, we generalize Kittel-Pincus theories of the SSW in ferromagnetic thin films to the case of non-collinear helimagnet with the surface end spins which are softly pinned by an anisotropy field. Consequently, we found there appear two types of modes. One is a Pincus mode which is composed of a long-period Bloch wave and a short-period ripple originated from the periodic structure of the CSL. Another is a short-period Kittel ripple excited by space-periodic perturbation which exists only in the case where the ac field is applied perpendicular the chiral axis. We demonstrate that the existence of the Pincus mode and the Kittel ripple is consistent with experimentally found double resonance profile.

Heating of a Quiet Region of the Solar Chromosphere by Ion and Neutral Acoustic Waves

Using high-resolution numerical simulations we investigate the plasma heating driven by periodic two-fluid acoustic waves that originate at the bottom of the photosphere and propagate into the gravitationally stratified and partially ionized solar atmosphere. We consider ions+electrons and neutrals as separate fluids that interact between themselves via collision forces. The latter play an important role in the chromosphere, leading to significant damping of short-period waves. Long-period waves do not essentially alter the photospheric temperatures, but they exhibit the capability of depositing a part of their energy in the chromosphere. This results in up about a five times increase of ion temperature that takes place there on a time-scale of a few minutes. The most effective heating corresponds to waveperiods within the range of about 30-200 s with a peak value located at 80 s. However, we conclude that for the amplitude of the driver chosen to be equal to 0.1 km s$^{-1}$, this heating is too low to balance the radiative losses in the chromosphere.

Tripod-Supported Offshore Wind Turbines: Modal and Coupled Analysis and a Parametric Study Using X-SEA and FAST

This paper presents theoretical aspects and an extensive numerical study of the coupled analysis of tripod support structures for offshore wind turbines (OWTs) by using X-SEA and FAST v8 programs. In a number of site conditions such as extreme and longer period waves, fast installation, and lighter foundations, tripod structures are more advantageous than monopile and jacket structures. In the implemented dynamic coupled analysis, the sub-structural module in FAST was replaced by the X-SEA offshore substructure analysis component. The time-histories of the reaction forces and the turbine loads were then calculated. The results obtained from X-SEA and from FAST were in good agreement. The pile-soil-structure interaction (PSSI) was included for reliable evaluation of OWT structural systems. The superelement concept was introduced to reduce the computational time. Modal, coupled and uncoupled analyses of the NREL 5MW OWT-tripod support structure including PSSI were carried out and the discussions on the natural frequencies, mode shapes and resulted displacements are presented. Compared to the uncoupled models, the physical interaction between the tower and the support structure in the coupled models resulted in smaller responses. Compared to the fixed support structures, i.e., when PSSI is not included, the piled-support structure has lower natural frequencies and larger responses attributed to its actual flexibility. The models using pile superelements are computationally efficient and give results that are identical to the common finite element models.

Stress-wave change in the copper structure: covering magnetic response

The work presents the results of the investigationof deformation processes occurring in copper after stress-wave influence. Structural changes analysis is carried out by direct research methods (X-ray phase analysis and optical microscopy) along and perpendicular to the spreading direction of the stress wave front in the copper foil plane. For more information, investigations have been conducted by an indirect method using ferromagnetic resonance of magnetic characteristics. As a magnetic covering, Co/Ni-type multilayer films are deposited on the copper foil, which makes it possible to apply magnetic research methods. The magnetic response of the multilayer covering correlates with the modification of the copper structure observed by direct methods. The information obtained in the course of research allows us to conclude that the wave character of the deformation processes occurring in copper is natural. The value and direction of structural modifications vary along the sample length as a function with a long-wave period is about 30 mm, which is consistent with the inhomogeneous distribution model of internal stresses. Throughout the sample length, alternating areas of stretching and compression of copper grains are fixed along the spreading direction of the stress wave front. The greatest stretching of the structural elements is observed at a distance equal to almost half the wavelength of the mechanical deformation field. Thus, the translational (shear) mode of the mechanical field of material plastic flow appears as the results of the investigation.

Dynamic Behavior of Ground Improved Using a Crushed Stone Foundation Wall

The improvement of soft clay and dredged soils to carry structures is increasingly important. In this study, the dynamic behavior of a crushed stone foundation wall in clay soil was analyzed using a 1g shaking table test. The response accelerations and spectra for three input ground motions were analyzed relative to the distance from the foundation wall, confirming that the acceleration was damped from the outside. The acceleration according to the distance from the wall was not significant under long-period motions, while different responses were obtained under short-period motions. The increased ground stiffness provided by the crushed stone wall lowered the natural period of the ground, and the acceleration amplification under short-period seismic waves was larger than that under long-period waves. Finally, equations were derived to describe the relationship between the acceleration amplification ratio and distance from the wall. The slopes of the proposed equations are larger under shorter periods, implying that the change in acceleration change with distance from the wall is more significant under shorter periods. The results of this study can be used to inform the design of soft soil improvements and the structures built atop them.

Wave Force Characteristics of Large-Sized Offshore Wind Support Structures to Sea Levels and Wave Conditions

This paper presents the results of wave force tests conducted on three types of offshore support structures considering eight waves and three sea levels to investigate the corresponding wave forces. As a result of this study, it is found that the occurrence of shoaling in shallow water induces a significant increase of the wave force. Most of the test models at the shallow water undergo a nonlinear increase of the wave force with higher wave height increasing. In addition, the larger the diameter of the support structure within the range of this study, the larger the diffraction effect is, and the increase in wave force due to shoaling is suppressed. Under an irregular wave at the shallow water, the wave force to the long-period wave tends to be slightly higher than that of the short period wave since the higher wave height component included in the irregular wave has an influence on the shoaling. In addition, it is found that the influence of shoaling under irregular wave becomes more apparent in the long period.

Dynamic Responses of Sliding Isolation Concrete Liquid Storage Tank under Far-Field Long-Period Earthquake

Under far-field long-period earthquake, liquid storage tanks are easy to be failure because of large amplitude liquid sloshing. In this paper, nonlinear contact is used to simulate behavior of sliding isolation bearing, nonlinear dynamic equation is used to solve fluid-structure interaction, bilinear material model is used to simulate limiting-device, and 3-D calculation model of sliding isolation concrete rectangular liquid storage tank (CRLST) with limiting-devices is established. Firstly, artificial far-field long-period earthquake waves are synthesized based on the existing seismic records. Secondly, dynamic responses of sliding isolation CRLST under the action of short-period and far-field long-period earthquakes are studied. Thirdly, effects of bi-directional earthquake and structure size on dynamic responses are investigated. Lastly, displacement control measures are discussed. Results show that far-field long-period earthquakes mainly affect horizontal displacement of structure and liquid sloshing wave height, and sliding isolation has obvious control effect on liquid sloshing wave height. Besides, horizontal displacement of structure and liquid sloshing wave height are increased with increase of seismic dimension and structure size. The reasonable designs of sliding isolation bearing and limiting-device can solve the problem that the maximum horizontal displacement of sliding isolation CRLST may exceed the limit under far-field long-period earthquake.

The use of parallel computing for the high-resolution determination of earthquake source parameters

Alongside the determination of the focal mechanism and source depth of an earthquake by direct examination of their probable values on a grid in the parameter space, also the resolution of these determinations can be estimated. However, this approach requires considerable time in the case of a detailed search. A special case of a shallow earthquake whose one nodal plane is subhorizontal is an example of the sources that require the use of a detailed grid. For studying these events based on the records of the long-period surface waves, the grids with high degree of detail in the angles of the focal mechanism are required. We discuss the application of the methods of parallel computing for speeding up the calculations of earthquake parameters and present the results of studying the strongest aftershock of the Tohoku, Japan, earthquake by this approach.

Blade dynamics in combined waves and current

Submerged aquatic vegetation (SAV), such as seagrass, is flexible and reconfigures (bends) in response to waves and current. The blade motion and reconfiguration modify the hydrodynamic drag. The modified drag can be described by an effective blade length, le, which is defined as the length of a rigid blade that results in the same drag as a flexible blade of length l. In many natural settings SAV is exposed to combinations of waves and current. This study derived and used laboratory measurements to validate new predictions of effective blade length for combined waves and current based on a Cauchy number, which describes the ratio of hydrodynamic drag to the restoring force due to rigidity of blade. Force measurements on and digital images of blades exposed to waves with a 2-s period and with a range of wave velocity (Uw) and current speed (Uc) were used to estimate the effective blade length. The measurements were also used to validate a numerical simulation of blade motion. Once validated, the simulation was used to expand the investigated parameter space to a wider range of wave conditions, and in particular longer wave periods. ForUc<14Uw, the blade motion and hydrodynamic drag were wave-dominated. For Uc>2Uw, the blade motion and hydrodynamic drag were current-dominated.

Two ‘faces’ of ENSO-induced surface waves during the tropical cyclone season

The response of the wave climate to tropical cyclones (TCs) is investigated using the significant wave height (SWH) observed from satellites and the WAVEWATCH III (WW3) model. Tropical cyclone wind generates local waves (wind seas) under the TC and longer-period waves (swells) that propagate long distances. The genesis location, intensity, and frequency of tropical cyclones over the global ocean are strongly affected by the phases of the El Niño Southern Oscillation (ENSO). It is shown that the interannual variation of global ocean surface waves in the subtropics during summer is dominated by ENSO-related TC activity. In particular, in the subtropical western North Pacific, the wind power is stronger in the TC season before an El Niño and weaker before a La Niña. These ENSO-related TC variations are shown, through composite and empirical orthogonal function analyses, as well as modeling, to dominate the spatial distribution and temporal variation of the SWH over the western North Pacific. The model confirms that longer-period waves (swells) are driven into northern South China Sea, toward Japan in mid latitudes and toward the central Pacific along the equator due to ENSO-related TC activities. The wind power and SWH over the subtropical western North Pacific lead and regress well with the ENSO index, suggesting that they may potentially serve as useful ENSO predictors.

Experimental study on the hydrodynamic performance of rectangular floating breakwater influenced by reef areas

In this paper, series of experimental studies under regular wave actions to investigate the hydrodynamic performance of the rectangular floating breakwater (FB) affected by reefs with different slopes were carried out in a wave flume. The wave transmission coefficients, motion responses and mooring forces can be calculated on the basis of the data obtained from the experiments. A comparative experiment of the only rectangular FB is also conducted. The experimental results reveal that the rectangular FB with different reefs can make more positive effects on wave energy dissipation than that of the only rectangular FB, especially for short-period waves. The characteristics of three degrees of freedom of the rectangular FB affected by reefs are also observed, which can be used to further explain the variation tendency appeared in transmission coefficients. The roll motion of the FB influenced by reefs is intenser than that of the only FB and the changes of slopes have limited effects on the sway motion of the FB. Furthermore, the heave motion of the only rectangular FB is intenser than that of the FB affected by reefs for short-period waves and vice versa for long-period waves.