Kwok Fai Cheung

Homotopy analysis of nonlinear progressive waves in deep water

This paper describes the application of a recently developed analytic approach known as the homotopy analysis method to derive a solution for the classical problem of nonlinear progressive waves in deep water. The method is based on a continuous variation from an initial trial to the exact solution. A Maclaurin series expansion provides a successive approximation of the solution through repeated application of a differential operator with the initial trial as the first term. This approach does not require the use of perturbation parameters and the solution series converges rapidly with the number of terms. In the framework of this approach, a new technique to apply the Padé expansion is implemented to further improve the convergence. As a result, the calculated phase speed at the 20th-order approximation of the solution agrees well with previous perturbation solutions of much higher orders and reproduces the well-known characteristics of being a non-monotonic function of wave steepness near the limiting condition.

Modeling near‐field tsunami observations to improve finite‐fault slip models for the 11 March 2011 Tohoku earthquake

The massive tsunami generated by the 11 March 2011 Tohoku earthquake (M_w 9.0) was widely recorded by GPS buoys, wave gauges, and ocean bottom pressure sensors around the source. Numerous inversions for finite-fault slip time histories have been performed using seismic and/or geodetic observations, yielding generally consistent patterns of large co-seismic slip offshore near the hypocenter and/or up-dip near the trench, where estimated peak slip is ~60 m. Modeling the tsunami generation and near-field wave processes using two detailed rupture models obtained from either teleseismic P waves or high-rate GPS recordings in Japan allows evaluation of how well the finite-fault models account for the regional tsunami data. By determining sensitivity of the tsunami calculations to rupture model features, we determine model modifications that improve the fit to the diverse tsunami data while retaining the fit to the seismic and geodetic observations.

Modeling of tropical cyclone winds and waves for emergency management

This paper compares three commonly used parametric models of tropical cyclone winds and evaluates their application in the wave model WAM. The parametric models provide surface wind fields based on best tracks of tropical cyclones and WAM simulates wave growth based on the wind energy input. The model package is applied to hindcast the wind and wave conditions of Hurricane Iniki, which directly hit the Hawaiian Island of Kauai in 1992. The parametric wind fields are evaluated against buoy and aircraft measurements made during the storm. A sensitivity analysis determines the spatial and spectral resolution needed to model the wave field of Hurricane Iniki. Comparisons of the modeled waves with buoy measurements indicate good agreement within the core of the storm and demonstrate the capability of the model package as a forecasting tool for emergency management.

The 25 October 2010 Mentawai tsunami earthquake (Mw 7.8) and the tsunami hazard presented by shallow megathrust ruptures

The 25 October 2010 Mentawai, Indonesia earthquake (M_w 7.8) ruptured the shallow portion of the subduction zone seaward of the Mentawai islands, off-shore of Sumatra, generating 3 to 9 m tsunami run-up along southwestern coasts of the Pagai Islands that took at least 431 lives. Analyses of teleseismic P, SH and Rayleigh waves for finite-fault source rupture characteristics indicate ∼90 s rupture duration with a low rupture velocity of ∼1.5 km/s on the 10° dipping megathrust, with total slip of 2–4 m over an ∼100 km long source region. The seismic moment-scaled energy release is 1.4 × 10^(−6), lower than 2.4 × 10^(−6) found for the 17 July 2006 Java tsunami earthquake (M_w 7.8). The Mentawai event ruptured up-dip of the slip region of the 12 September 2007 Kepulauan earthquake (M_w 7.9), and together with the 4 January 1907 (M 7.6) tsunami earthquake located seaward of Simeulue Island to the northwest along the arc, demonstrates the significant tsunami generation potential for shallow megathrust ruptures in regions up-dip of great underthrusting events in Indonesia and elsewhere.

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.

Resonance in Hawaii waters from the 2006 Kuril Islands Tsunami

[1] The 2006 Kuril Islands Tsunami, while not destructive to coastal properties, resulted in prolonged oscillations in Hawaii waters. This study examines the oscillation patterns and amplification through reconstruction of the tsunami using a nonlinear shallow-water model. After validation with water-level measurements, a Fast Fourier Transform of the computed surface elevation reveals profound oscillation modes at various periods around the Hawaiian Islands. The oscillation at the regional scale consists of standing waves across the island chain and resonance in interconnected channels, embayments, and shallow shelves. Resonance in embayments and standing edge waves dominate the oscillation in coastal waters. The results show strong correlation between bathymetric features and resonance oscillations and identify tsunami hazard areas for planning and emergency management.

Rupture process of the 2010 Mw 7.8 Mentawai tsunami earthquake from joint inversion of near-field hr-GPS and teleseismic body wave recordings constrained by tsunami observations

The 25 October 2010 Mentawai tsunami earthquake (Mw 7.8) ruptured the shallow portion of the Sunda megathrust seaward of the Mentawai Islands, offshore of Sumatra, Indonesia, generating a strong tsunami that took 509 lives. The rupture zone was updip of those of the 12 September 2007 Mw 8.5 and 7.9 underthrusting earthquakes. High-rate (1 s sampling) GPS instruments of the Sumatra GPS Array network deployed on the Mentawai Islands and Sumatra mainland recorded time-varying and static ground displacements at epicentral distances from 49 to 322 km. Azimuthally distributed tsunami recordings from two deepwater sensors and two tide gauges that have local high-resolution bathymetric information provide additional constraints on the source process. Finite-fault rupture models, obtained by joint inversion of the high-rate (hr)-GPS time series and numerous teleseismic broadband P and S wave seismograms together with iterative forward modeling of the tsunami recordings, indicate rupture propagation ~50 km up dip and ~100 km northwest along strike from the hypocenter, with a rupture velocity of ~1.8 km/s. Subregions with large slip extend from 7 to 10 km depth ~80 km northwest from the hypocenter with a maximum slip of 8 m and from ~5 km depth to beneath thin horizontal sedimentary layers beyond the prism deformation front for ~100 km along strike, with a localized region having >15 m of slip. The seismic moment is 7.2 × 1020 N m. The rupture model indicates that local heterogeneities in the shallow megathrust can accumulate strain that allows some regions near the toe of accretionary prisms to fail in tsunami earthquakes.

Second order wave diffraction around two-dimensional bodies by time-domain method*

A time-domain second order method is developed to study the nonlinear wave forces and runupon a surface piercing body of arbitrary shape in two dimensions. The free surface boundary conditions and the radiation condition are satisfied to second order by a numerical integration in time and the field solution at each time step is obtained by an integral equation method based on Greens theorem. The solution is separated into a known incident potential and a scattered potential. The initial condition corresponds to a Stokes second order wave field in the domain, and the scattered potential is allowed to develop in time and space. The stability and numerical accuracy of the proposed solution and the treatment of the radiation condition to second order are discussed. Comparisons of wave forces are made with previous theoretical and experimental results for the case of a semi-circular cylinder with axis at the still water level and a favourable agreement is indicated.

Run-up on a structure due to second-order waves and a current in a numerical wave tank

A numerical wave tank is considered in which the interaction between waves, current and a structure is simulated by a 3D boundary element model in the time domain. Through a Taylor series expansion and a perturbation procedure the model is formulated to second order in wave steepness and to first order in current speed. The boundary-value problem is separated into a known incident wave field and an unknown scattered wave field, the latter being absorbed at the radiation boundaries using active wave absorption. The present paper focuses on the wave run-up on a structure in waves and current. For the simulations a bottom mounted vertical circular cylinder is chosen. The numerical results show good agreement with previous analytical and numerical solutions for second-order wave diffraction without a current and first-order wave diffraction with a collinear current. The inclusion of a current in the calculation of second-order wave run-up is new and the validity of the results is demonstrated by a parametric study. It is shown that both the current and the second-order wave components are of significant importance in calculating magnitude and location of the maximum run-up on a structure.

ADCP observations of edge waves off Oahu in the wake of the November 2006 Kuril Islands tsunami

Received 13 September 2007; revised 5 October 2007; accepted 8 November 2007; published 15 December 2007. [1] During the 2006 Kuril Islands tsunami, edge waves propagating along Oahu’s south shore were observed via depth-averaged ADCP velocity and pressure data acquired in real-time by a coastal observatory at 12 m depth and 400 m offshore. Time-varying rotary-component velocity spectra obtained via wavelet analysis agree with the phase lag observed between pressure and each Cartesian velocity component, in indicating the directions of rotation and travel of progressive edge waves. Furthermore, the theoretical ratios between power in the free surface elevation and in each velocity component of edge waves, agree with those observed, and a nonlinear shallow-water model shows edge waves of various modes propagating along the shore near our observation location. Importantly, the maximum surge in sea level occurred at a time when edge waves of all constituent frequencies were superposed. Citation: Bricker, J. D., S. Munger, C. Pequignet, J. R. Wells, G. Pawlak, and K. F. Cheung (2007), ADCP observations of edge waves off Oahu in the wake of the November 2006 Kuril Islands tsunami, Geophys. Res. Lett., 34, L23617, doi:10.1029/ 2007GL032015.