Guan-Yu Chen - Academia.edu (original) (raw)

Papers by Guan-Yu Chen

Research paper thumbnail of Seabed Scour Around a Breakwater a Case Study in Mailiao Harbor

Journal of Marine Science and Technology, Dec 1, 2015

Research paper thumbnail of Response to comments of Anonymous Referee #3 on “Reciprocal Green’s Functions and the Quick Forecast of Submarine Landslide Tsunami”

Research paper thumbnail of Response to comments of Xiaoming Wang on “Reciprocal Green’s Functions and the Quick Forecast of Submarine Landslide Tsunami”

Research paper thumbnail of Quick Estimation of Tsunami Induced Runup on Coastal Area

Coastal Engineering Proceedings, 2014

The main purpose of this study is that extending 1D Carrier-Wu-Yeh algorithm and analytical Green... more The main purpose of this study is that extending 1D Carrier-Wu-Yeh algorithm and analytical Green's function (AGF) to estimate the arbitrary irregular waveforms induced runup height and the inundation distance, and further builds a pre-calculated runup dataset. In this study, the multiplication and superposition is employed to replace the direct numerical integration. The waveforms are decomposed as numerous Fourier components using fast Fourier transformation. The corresponding mechanical energy can be calculated beforehand and save the results as a database-form. Using this process, the maximum runup height and the inundation distance can be quick calculated after determining the total mechanical energy. Based on application on the real tsunami events, the comparisons show that the present methodology can shorten the computing time in comparison with the direct numerical integration. Moreover, the present approach also applies on real tsunami events, 2004 Indian tsunami and 2011 Tohoku tsunami, to estimate the runup height and the inundation distance. The forecasted results are quite satisfactory in comparison with the field measurement, and it implies that the reasonable accuracy and the computing efficiency are both considered in this study. Keywords:1D Carrier-Wu-Yeh algorithm, analytical Green's function (AGF), 2004 Indian tsunami, 2011 Tohoku tsunami.

Research paper thumbnail of Derivation of internal solitary wave amplitude in the South China Sea deep basin from satellite images

Journal of Oceanography, 2011

In the present study, theories based on the Korteweg-de Vries equation are extended to the Benjam... more In the present study, theories based on the Korteweg-de Vries equation are extended to the Benjamin-Ono equation to allow the determination of internal solitary wave (ISW) amplitude from satellite images. The free surface flow induced by an ISW is derived for deep water. As a coherent structure, the amplitude of the ISW has a unique relation to the convergence/divergence of surface flow, such that the flow convergence/divergence will increase/decrease the backscattering cross section and generate bright/dark bands in satellite images. The distance between bright and dark bands can be related to the amplitude of ISW. To validate the theory, a multi-ship measurement made on 9-11 May 2005 during the spring tide period is used. A systematic approach to determine the thickness and density of the upper and lower layers is also included so that the free surface flow can be determined with a relatively high accuracy.

Research paper thumbnail of Observed near-surface currents under high wind speeds

Journal of Geophysical Research: Oceans, 2012

From the Surface Velocity Program (SVP) drifter current and QuikSCAT wind data, the relationship ... more From the Surface Velocity Program (SVP) drifter current and QuikSCAT wind data, the relationship between the observed near-surface current vectors and surface wind vectors for the northwestern Pacific Ocean under high winds (20-50 m s À1) are obtained with quantitative estimations of near-surface drift ratio (current speed versus wind speed) r ($2%) and near-surface drift angle a ($0-10 to the right of the winds). These estimations keep unchanged after removing the surface geostrophic component. From the SVP drifter current and daily WindSat wind data, the estimated r is still approximately 2%. Three linear regression equations are obtained between the observed near-surface current speeds and the surface wind stress for the high wind range.

Research paper thumbnail of Numerical Study on Tsunamis Excited by 2006 Pingtung Earthquake Doublet

Terrestrial, Atmospheric and Oceanic Sciences, 2008

The tsunami propagation and coastal run-ups generated by the 2006 Pingtung earthquake doublet is ... more The tsunami propagation and coastal run-ups generated by the 2006 Pingtung earthquake doublet is studied numerically. The numerical model-COMCOT, which adopts a modified LeapFrog finite difference scheme solving nonlinear Shallow Water Equations (NSWE), is employed. The assessment of the tsunami amplitude and extended effects is discussed in this paper using a set of nested bathymetric grids with a decreasing cell size focused on southern Taiwan. The three nested grids cover from the large far-field South-China Sea to the small near-shore regions. Several possible fault plane mechanisms are examined. Based on the arrival time at different tidal gauges, the suggested seafloor displacement is presented. Adopting the relocated seafloor movement with the fault parameters issued by Global CMT, the model results are favorably compared with the field tidal gauge wave form data. The result shows that the tsunami amplitude is about 35 cm and about 20-min period with the first depression at SyunGuaggZuei. A worse case scenario, M w = 8.0, is studied. The maximum water levels can reach 4 m for M w = 8.0 along the shoreline at HouBiHu. We also observe that owning to the source geometries and to the trapping of the tsunami energy by edge wave effect, the southeast coast of Taiwan coast is one of the most dangerous zones for the South China Sea earthquakes.

Research paper thumbnail of Diffraction Effects in a Phase-Averaged Wave Model

Unlike wave models which analyze each individual wave, phase-averaged wave models focus only on t... more Unlike wave models which analyze each individual wave, phase-averaged wave models focus only on the wave amplitude and can simulate a much larger area. However, its application to sheltered zone is limited because the diffraction effect is not included. To improve the phase-averaged wave model, the Geometrical Theory of Diffraction (GTD) is introduced and complex coastlines are replaced by simple geometries such as semi-infinite breakwaters or wedges. By expanding the exact solution with respect to the nondimensional distance to the pointed end of the wedge, kr, the diffraction wave could be represented by a source on the pointed end. The asymptotic solution for totally absorbent wedge boundaries is implemented in the NOAA Wave Watch Ⅲ (NWWⅢ) model as a new wave source at the end of the wedge. Two other approaches on implementing diffraction effect are also discussed.

Research paper thumbnail of Measuring Progressive Edge Wave by a Single Instrument: Applications in Tsunami and Typhoon Waves

If waves are generated in a restricted region far away along the coast, their direction is easy t... more If waves are generated in a restricted region far away along the coast, their direction is easy to determine. For a wave gage at a longand straight coastline, the measured wave can be classified into three ategories, viz. direct plane wave from the source, short-crested wave eflected once by the shoreline, and progressive edge wave repeatedly reflected and refracted along the coast. Traditionally, an edge wave is measured along a long and straight coast with a couple of pressure-gage/current-meter arrays to acquire the frequency-wavenumber dispersion diagram. In the present study, flow-pressure relations for both infragravity edge and short-crested waves are used to identify the edge wave mode. This new approach is a useful tool if there is just one dominating edge wave mode and the edge wave is propagating away from a known source. Edge wave tsunamis and infragravity storm waves are analyzed as two examples.

Research paper thumbnail of Quick Evaluation of Runup Height and Inundation Area for Early Warning of Tsunami

Journal of Earthquake and Tsunami, 2012

A methodology combining the offshore tsunami calculated by using numerical reciprocal Green's... more A methodology combining the offshore tsunami calculated by using numerical reciprocal Green's function (RGF) and the runup flow field calculated by using an analytical Green's function (AGF) is proposed to quickly estimate a tsunami hazard. For a vulnerable city, the RGF is computed previously via linear shallow water equations over real bathymetry and the offshore tsunami can be obtained promptly once the initial rupture is known. A transformation from time to space is then applied to obtain an equivalent waveform. With an integral with the AGF, derived by Carrier et al. [2003] based on 1D fully nonlinear shallow water equations over a uniform constant slope, the runup flow field is calculated. Thus, besides saving computation time and reducing the memory requirement, the desired initial condition for the AGF can also be generate by RGF. In this approach, the max wave height and the inundation distance are estimated very quickly and can be applied to broadcast an early warn...

Research paper thumbnail of Combining Tsunami Hazard and Vulnerability on the Assessment of Tsunami Inundation Probability in Taiwan

Journal of Earthquake and Tsunami, 2014

As earthquake and tsunami are closely related, the probability of tsunami hazard had been done by... more As earthquake and tsunami are closely related, the probability of tsunami hazard had been done by extending the approach used in earthquakes. However, the hazard of tsunami depends also on the vulnerability of neighboring structures and hence its hazard and vulnerability should not be assessed separately. The distribution of tsunami height varies so significantly that the traditional definition parallel to that in seismic risk should be modified. Besides, previous studies on the probability of tsunami focused on the occurrence possibility of tsunami hazard in a fixed period of time, but this information is not applicable for a specific tsunami incidence. For the above-mentioned problems, a new algorithm that comprises two components is proposed in the present study. The first component, the Probabilistic Forecast of Tsunami Inundation (PFTI), is the conditional inundation probability once a tsunami of a specific height occurs, or an earthquake is detected at some specific location w...

Research paper thumbnail of Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (“Ostrovsky”) equation

Wave Motion, 2002

The rotation-modified Korteweg-de Vries (RMKdV) equation differs from the ordinary KdV equation o... more The rotation-modified Korteweg-de Vries (RMKdV) equation differs from the ordinary KdV equation only through an extra undifferentiated term due to Coriolis force. This article describes the steadily travelling, spatially periodic solutions which have peaks of identical size. These generalize the "cnoidal" waves of the KdV equation. There are five overlapping regimes in the parameter space. We derive four different analytical approximations to interpret them. There is also a narrow region where the solution folds over so that there are three distinct shapes at a given point in parameter space. The shortest of these shapes is approximated everywhere in space by a parabola except for a thin interior layer at the crest. A low-order Fourier-Galerkin algorithm, usually thought of as a numerical method, also yields an explicit analytic approximation, too. We illustrate the usefulness of these approximations through comparisons with pseudospectral Fourier numerical computations over the whole parameter space.

Research paper thumbnail of A three-dimensional wave field over a bidirectionally periodic ripple bottom

Ocean Engineering, 2007

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is de... more For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the second order so that the Bragg resonance effect of the ripple bottom on the free-surface wave can be analyzed. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is avoided. This theory is successfully verified by reducing to simpler situations. Then, the analytical results for the special case of a unidirectional sinusoidal bottom are compared with experimental data for validation.

Research paper thumbnail of Resonance Induced by Edge Waves in Hua-Lien Harbor

Journal of Oceanography, 2004

This article first reviews previous numerical studies on the resonance problem of Hua-Lien Harbor... more This article first reviews previous numerical studies on the resonance problem of Hua-Lien Harbor. All the research leads to the conclusion that resonance can be stimulated by 2-D infragravity waves. However, a literature survey suggests that outside the harbor these plane infragravity waves are too small to excite violent water-body movement inside. On the other hand, 3-D infragravity waves trapped along the coastline, also known as edge waves, are more likely to exist outside the harbor and their effect needs to be thoroughly discussed. Based on previous measurements, the response of Hua-Lien Harbor is best simulated using edge waves of 160 and 140 second periods and their resonance mechanisms are analyzed. The former case has a longitudinal resonant mode and hence the amplitude in the inner harbor is large. The latter case has a transverse mode in the outer basin and hence only berths in the outer basin are influenced. These features are both consistent with field measurement. Therefore, it is very likely that edge waves are responsible for the resonance of Hua-Lien Harbor. Finally, based on observation after the construction of the present offshore breakwaters, a theory is proposed to explain the trapping of incident edge waves, and a measure to further reduce the resonance is discussed. which has a frequency lower than that of red light. The infragravity wave can be classified into two categories, viz. 2-D and 3-D infragravity waves. The 3-D waves are trapped at the edge of the sea; hence, they are usually called edge waves; the 2-D waves have uniform amplitude in the direction normal to their propagation. Some infragravity waves propagate freely, just like common gravity waves, but it is also possible that some are bound and move with the wave groups due to nonlinear effects. Oscillations of this kind are called bound waves. The existence of the infragravity wave outside Hua-Lien Harbor is validated by the measurement of the Institute of Harbor and Marine Technology (IHMT). However, these measurements cannot be directly applied as the forcing of the harbor resonance, for the following reasons. First, a single instrument means that it is impossible to tell whether the component belongs to the incident wave or the reflected one. Only the former can force the harbor to oscillate. Similarly, a single instrument gives no information on the exact spatial distribution of the long-wave component. Either a plane wave or a trapped edge wave can produce an infragravity wave. According to the reasoning above, the infragravity component of the wave record cannot be directly interpreted as a plane incident free wave.

Research paper thumbnail of Forecast System for Offshore Water Surface Elevation With Inundation Map Integrated for Tsunami Early Warning

IEEE Journal of Oceanic Engineering, 2000

Research paper thumbnail of Effect of Cylindrically Shaped Atoll on Westward-Propagating Anticyclonic Eddy—A Case Study

IEEE Geoscience and Remote Sensing Letters, 2000

Mesoscale anticyclonic eddies occasionally propagate westward across the Dongsha atoll situated o... more Mesoscale anticyclonic eddies occasionally propagate westward across the Dongsha atoll situated on the continental slope in the northern South China Sea (SCS). Satellite observations of this phenomenon are used to identify eddy weakening and deforming. Stronger anticyclonic eddies are weakening within a distance of 30–120 km from the atoll. A weaker anticyclone with an eddy diameter of 120 km, a sea-level slope of 8.3times10−88.3 \times 10^{-8}8.3times108, a Reynolds number of 17, and a slow moving speed (2.5 km/d) in the SCS can be split into two smaller eddies.

Research paper thumbnail of Progressive Waves in Real Fluids Over a Rigid Permeable Bottom

Coastal Engineering Journal, 2010

Abstract: This report deals with the slipping friction in a progressive wave of real fluids propa... more Abstract: This report deals with the slipping friction in a progressive wave of real fluids propagating over a permeable bottom. Because the" no-slip" condition is usually considered in the wave motion, the horizontal velocity at the seabed is assumed zero. However, ...

Research paper thumbnail of Nonlinear wave packets of equatorial Kelvin waves

Geophysical & Astrophysical Fluid Dynamics, 2002

The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular per... more The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular perturbation theory applied to the shallow water wave equations. Within the limits of the perturbation theory, which is formally restricted to weak mean shear and weak ...

Research paper thumbnail of Observed near-surface flows under all tropical cyclone intensity levels using drifters in the northwestern Pacific

[1] Data from drifters of the surface velocity program and tropical cyclones (TCs) of the Joint T... more [1] Data from drifters of the surface velocity program and tropical cyclones (TCs) of the Joint Typhoon Warning Center during 1985–2009 were analyzed to demonstrate strong currents under various storm intensities such as category-4 to −5, category-2 to −3, and tropical storm to category-1 TCs in the northwestern Pacific. Current speeds over 2.0 m s−1 are observed under major TCs with the strongest mean currents to the right of the storm track. This study provides the characterization of the near-surface velocity response to all recorded TCs, and agrees roughly with Geisler's theory (1970). Our observations also verify earlier modeling results of Price (1983).

Research paper thumbnail of Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection

Mathematics and computers in simulation, 2001

If the initial condition for the Korteweg–de Vries (KdV) equation is a weakly nonlinear wavepacke... more If the initial condition for the Korteweg–de Vries (KdV) equation is a weakly nonlinear wavepacket, then its evolution is described by the nonlinear Schrödinger (NLS) equation. This KdV/NLS connection has been known for many years, but its various aspects and ...

Research paper thumbnail of Seabed Scour Around a Breakwater a Case Study in Mailiao Harbor

Journal of Marine Science and Technology, Dec 1, 2015

Research paper thumbnail of Response to comments of Anonymous Referee #3 on “Reciprocal Green’s Functions and the Quick Forecast of Submarine Landslide Tsunami”

Research paper thumbnail of Response to comments of Xiaoming Wang on “Reciprocal Green’s Functions and the Quick Forecast of Submarine Landslide Tsunami”

Research paper thumbnail of Quick Estimation of Tsunami Induced Runup on Coastal Area

Coastal Engineering Proceedings, 2014

The main purpose of this study is that extending 1D Carrier-Wu-Yeh algorithm and analytical Green... more The main purpose of this study is that extending 1D Carrier-Wu-Yeh algorithm and analytical Green's function (AGF) to estimate the arbitrary irregular waveforms induced runup height and the inundation distance, and further builds a pre-calculated runup dataset. In this study, the multiplication and superposition is employed to replace the direct numerical integration. The waveforms are decomposed as numerous Fourier components using fast Fourier transformation. The corresponding mechanical energy can be calculated beforehand and save the results as a database-form. Using this process, the maximum runup height and the inundation distance can be quick calculated after determining the total mechanical energy. Based on application on the real tsunami events, the comparisons show that the present methodology can shorten the computing time in comparison with the direct numerical integration. Moreover, the present approach also applies on real tsunami events, 2004 Indian tsunami and 2011 Tohoku tsunami, to estimate the runup height and the inundation distance. The forecasted results are quite satisfactory in comparison with the field measurement, and it implies that the reasonable accuracy and the computing efficiency are both considered in this study. Keywords:1D Carrier-Wu-Yeh algorithm, analytical Green's function (AGF), 2004 Indian tsunami, 2011 Tohoku tsunami.

Research paper thumbnail of Derivation of internal solitary wave amplitude in the South China Sea deep basin from satellite images

Journal of Oceanography, 2011

In the present study, theories based on the Korteweg-de Vries equation are extended to the Benjam... more In the present study, theories based on the Korteweg-de Vries equation are extended to the Benjamin-Ono equation to allow the determination of internal solitary wave (ISW) amplitude from satellite images. The free surface flow induced by an ISW is derived for deep water. As a coherent structure, the amplitude of the ISW has a unique relation to the convergence/divergence of surface flow, such that the flow convergence/divergence will increase/decrease the backscattering cross section and generate bright/dark bands in satellite images. The distance between bright and dark bands can be related to the amplitude of ISW. To validate the theory, a multi-ship measurement made on 9-11 May 2005 during the spring tide period is used. A systematic approach to determine the thickness and density of the upper and lower layers is also included so that the free surface flow can be determined with a relatively high accuracy.

Research paper thumbnail of Observed near-surface currents under high wind speeds

Journal of Geophysical Research: Oceans, 2012

From the Surface Velocity Program (SVP) drifter current and QuikSCAT wind data, the relationship ... more From the Surface Velocity Program (SVP) drifter current and QuikSCAT wind data, the relationship between the observed near-surface current vectors and surface wind vectors for the northwestern Pacific Ocean under high winds (20-50 m s À1) are obtained with quantitative estimations of near-surface drift ratio (current speed versus wind speed) r ($2%) and near-surface drift angle a ($0-10 to the right of the winds). These estimations keep unchanged after removing the surface geostrophic component. From the SVP drifter current and daily WindSat wind data, the estimated r is still approximately 2%. Three linear regression equations are obtained between the observed near-surface current speeds and the surface wind stress for the high wind range.

Research paper thumbnail of Numerical Study on Tsunamis Excited by 2006 Pingtung Earthquake Doublet

Terrestrial, Atmospheric and Oceanic Sciences, 2008

The tsunami propagation and coastal run-ups generated by the 2006 Pingtung earthquake doublet is ... more The tsunami propagation and coastal run-ups generated by the 2006 Pingtung earthquake doublet is studied numerically. The numerical model-COMCOT, which adopts a modified LeapFrog finite difference scheme solving nonlinear Shallow Water Equations (NSWE), is employed. The assessment of the tsunami amplitude and extended effects is discussed in this paper using a set of nested bathymetric grids with a decreasing cell size focused on southern Taiwan. The three nested grids cover from the large far-field South-China Sea to the small near-shore regions. Several possible fault plane mechanisms are examined. Based on the arrival time at different tidal gauges, the suggested seafloor displacement is presented. Adopting the relocated seafloor movement with the fault parameters issued by Global CMT, the model results are favorably compared with the field tidal gauge wave form data. The result shows that the tsunami amplitude is about 35 cm and about 20-min period with the first depression at SyunGuaggZuei. A worse case scenario, M w = 8.0, is studied. The maximum water levels can reach 4 m for M w = 8.0 along the shoreline at HouBiHu. We also observe that owning to the source geometries and to the trapping of the tsunami energy by edge wave effect, the southeast coast of Taiwan coast is one of the most dangerous zones for the South China Sea earthquakes.

Research paper thumbnail of Diffraction Effects in a Phase-Averaged Wave Model

Unlike wave models which analyze each individual wave, phase-averaged wave models focus only on t... more Unlike wave models which analyze each individual wave, phase-averaged wave models focus only on the wave amplitude and can simulate a much larger area. However, its application to sheltered zone is limited because the diffraction effect is not included. To improve the phase-averaged wave model, the Geometrical Theory of Diffraction (GTD) is introduced and complex coastlines are replaced by simple geometries such as semi-infinite breakwaters or wedges. By expanding the exact solution with respect to the nondimensional distance to the pointed end of the wedge, kr, the diffraction wave could be represented by a source on the pointed end. The asymptotic solution for totally absorbent wedge boundaries is implemented in the NOAA Wave Watch Ⅲ (NWWⅢ) model as a new wave source at the end of the wedge. Two other approaches on implementing diffraction effect are also discussed.

Research paper thumbnail of Measuring Progressive Edge Wave by a Single Instrument: Applications in Tsunami and Typhoon Waves

If waves are generated in a restricted region far away along the coast, their direction is easy t... more If waves are generated in a restricted region far away along the coast, their direction is easy to determine. For a wave gage at a longand straight coastline, the measured wave can be classified into three ategories, viz. direct plane wave from the source, short-crested wave eflected once by the shoreline, and progressive edge wave repeatedly reflected and refracted along the coast. Traditionally, an edge wave is measured along a long and straight coast with a couple of pressure-gage/current-meter arrays to acquire the frequency-wavenumber dispersion diagram. In the present study, flow-pressure relations for both infragravity edge and short-crested waves are used to identify the edge wave mode. This new approach is a useful tool if there is just one dominating edge wave mode and the edge wave is propagating away from a known source. Edge wave tsunamis and infragravity storm waves are analyzed as two examples.

Research paper thumbnail of Quick Evaluation of Runup Height and Inundation Area for Early Warning of Tsunami

Journal of Earthquake and Tsunami, 2012

A methodology combining the offshore tsunami calculated by using numerical reciprocal Green's... more A methodology combining the offshore tsunami calculated by using numerical reciprocal Green's function (RGF) and the runup flow field calculated by using an analytical Green's function (AGF) is proposed to quickly estimate a tsunami hazard. For a vulnerable city, the RGF is computed previously via linear shallow water equations over real bathymetry and the offshore tsunami can be obtained promptly once the initial rupture is known. A transformation from time to space is then applied to obtain an equivalent waveform. With an integral with the AGF, derived by Carrier et al. [2003] based on 1D fully nonlinear shallow water equations over a uniform constant slope, the runup flow field is calculated. Thus, besides saving computation time and reducing the memory requirement, the desired initial condition for the AGF can also be generate by RGF. In this approach, the max wave height and the inundation distance are estimated very quickly and can be applied to broadcast an early warn...

Research paper thumbnail of Combining Tsunami Hazard and Vulnerability on the Assessment of Tsunami Inundation Probability in Taiwan

Journal of Earthquake and Tsunami, 2014

As earthquake and tsunami are closely related, the probability of tsunami hazard had been done by... more As earthquake and tsunami are closely related, the probability of tsunami hazard had been done by extending the approach used in earthquakes. However, the hazard of tsunami depends also on the vulnerability of neighboring structures and hence its hazard and vulnerability should not be assessed separately. The distribution of tsunami height varies so significantly that the traditional definition parallel to that in seismic risk should be modified. Besides, previous studies on the probability of tsunami focused on the occurrence possibility of tsunami hazard in a fixed period of time, but this information is not applicable for a specific tsunami incidence. For the above-mentioned problems, a new algorithm that comprises two components is proposed in the present study. The first component, the Probabilistic Forecast of Tsunami Inundation (PFTI), is the conditional inundation probability once a tsunami of a specific height occurs, or an earthquake is detected at some specific location w...

Research paper thumbnail of Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (“Ostrovsky”) equation

Wave Motion, 2002

The rotation-modified Korteweg-de Vries (RMKdV) equation differs from the ordinary KdV equation o... more The rotation-modified Korteweg-de Vries (RMKdV) equation differs from the ordinary KdV equation only through an extra undifferentiated term due to Coriolis force. This article describes the steadily travelling, spatially periodic solutions which have peaks of identical size. These generalize the "cnoidal" waves of the KdV equation. There are five overlapping regimes in the parameter space. We derive four different analytical approximations to interpret them. There is also a narrow region where the solution folds over so that there are three distinct shapes at a given point in parameter space. The shortest of these shapes is approximated everywhere in space by a parabola except for a thin interior layer at the crest. A low-order Fourier-Galerkin algorithm, usually thought of as a numerical method, also yields an explicit analytic approximation, too. We illustrate the usefulness of these approximations through comparisons with pseudospectral Fourier numerical computations over the whole parameter space.

Research paper thumbnail of A three-dimensional wave field over a bidirectionally periodic ripple bottom

Ocean Engineering, 2007

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is de... more For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the second order so that the Bragg resonance effect of the ripple bottom on the free-surface wave can be analyzed. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is avoided. This theory is successfully verified by reducing to simpler situations. Then, the analytical results for the special case of a unidirectional sinusoidal bottom are compared with experimental data for validation.

Research paper thumbnail of Resonance Induced by Edge Waves in Hua-Lien Harbor

Journal of Oceanography, 2004

This article first reviews previous numerical studies on the resonance problem of Hua-Lien Harbor... more This article first reviews previous numerical studies on the resonance problem of Hua-Lien Harbor. All the research leads to the conclusion that resonance can be stimulated by 2-D infragravity waves. However, a literature survey suggests that outside the harbor these plane infragravity waves are too small to excite violent water-body movement inside. On the other hand, 3-D infragravity waves trapped along the coastline, also known as edge waves, are more likely to exist outside the harbor and their effect needs to be thoroughly discussed. Based on previous measurements, the response of Hua-Lien Harbor is best simulated using edge waves of 160 and 140 second periods and their resonance mechanisms are analyzed. The former case has a longitudinal resonant mode and hence the amplitude in the inner harbor is large. The latter case has a transverse mode in the outer basin and hence only berths in the outer basin are influenced. These features are both consistent with field measurement. Therefore, it is very likely that edge waves are responsible for the resonance of Hua-Lien Harbor. Finally, based on observation after the construction of the present offshore breakwaters, a theory is proposed to explain the trapping of incident edge waves, and a measure to further reduce the resonance is discussed. which has a frequency lower than that of red light. The infragravity wave can be classified into two categories, viz. 2-D and 3-D infragravity waves. The 3-D waves are trapped at the edge of the sea; hence, they are usually called edge waves; the 2-D waves have uniform amplitude in the direction normal to their propagation. Some infragravity waves propagate freely, just like common gravity waves, but it is also possible that some are bound and move with the wave groups due to nonlinear effects. Oscillations of this kind are called bound waves. The existence of the infragravity wave outside Hua-Lien Harbor is validated by the measurement of the Institute of Harbor and Marine Technology (IHMT). However, these measurements cannot be directly applied as the forcing of the harbor resonance, for the following reasons. First, a single instrument means that it is impossible to tell whether the component belongs to the incident wave or the reflected one. Only the former can force the harbor to oscillate. Similarly, a single instrument gives no information on the exact spatial distribution of the long-wave component. Either a plane wave or a trapped edge wave can produce an infragravity wave. According to the reasoning above, the infragravity component of the wave record cannot be directly interpreted as a plane incident free wave.

Research paper thumbnail of Forecast System for Offshore Water Surface Elevation With Inundation Map Integrated for Tsunami Early Warning

IEEE Journal of Oceanic Engineering, 2000

Research paper thumbnail of Effect of Cylindrically Shaped Atoll on Westward-Propagating Anticyclonic Eddy—A Case Study

IEEE Geoscience and Remote Sensing Letters, 2000

Mesoscale anticyclonic eddies occasionally propagate westward across the Dongsha atoll situated o... more Mesoscale anticyclonic eddies occasionally propagate westward across the Dongsha atoll situated on the continental slope in the northern South China Sea (SCS). Satellite observations of this phenomenon are used to identify eddy weakening and deforming. Stronger anticyclonic eddies are weakening within a distance of 30–120 km from the atoll. A weaker anticyclone with an eddy diameter of 120 km, a sea-level slope of 8.3times10−88.3 \times 10^{-8}8.3times108, a Reynolds number of 17, and a slow moving speed (2.5 km/d) in the SCS can be split into two smaller eddies.

Research paper thumbnail of Progressive Waves in Real Fluids Over a Rigid Permeable Bottom

Coastal Engineering Journal, 2010

Abstract: This report deals with the slipping friction in a progressive wave of real fluids propa... more Abstract: This report deals with the slipping friction in a progressive wave of real fluids propagating over a permeable bottom. Because the" no-slip" condition is usually considered in the wave motion, the horizontal velocity at the seabed is assumed zero. However, ...

Research paper thumbnail of Nonlinear wave packets of equatorial Kelvin waves

Geophysical & Astrophysical Fluid Dynamics, 2002

The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular per... more The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular perturbation theory applied to the shallow water wave equations. Within the limits of the perturbation theory, which is formally restricted to weak mean shear and weak ...

Research paper thumbnail of Observed near-surface flows under all tropical cyclone intensity levels using drifters in the northwestern Pacific

[1] Data from drifters of the surface velocity program and tropical cyclones (TCs) of the Joint T... more [1] Data from drifters of the surface velocity program and tropical cyclones (TCs) of the Joint Typhoon Warning Center during 1985–2009 were analyzed to demonstrate strong currents under various storm intensities such as category-4 to −5, category-2 to −3, and tropical storm to category-1 TCs in the northwestern Pacific. Current speeds over 2.0 m s−1 are observed under major TCs with the strongest mean currents to the right of the storm track. This study provides the characterization of the near-surface velocity response to all recorded TCs, and agrees roughly with Geisler's theory (1970). Our observations also verify earlier modeling results of Price (1983).

Research paper thumbnail of Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection

Mathematics and computers in simulation, 2001

If the initial condition for the Korteweg–de Vries (KdV) equation is a weakly nonlinear wavepacke... more If the initial condition for the Korteweg–de Vries (KdV) equation is a weakly nonlinear wavepacket, then its evolution is described by the nonlinear Schrödinger (NLS) equation. This KdV/NLS connection has been known for many years, but its various aspects and ...