Tai-Wen Hsu

Simulating typhoon waves by SWAN wave model in coastal waters of Taiwan

The SWAN wave model is typically designed for wave simulations in the near-shore region and thus is selected for evaluating its applicability on typhoon waves in the coastal waters around Taiwan Island. Numerical calculations on processes of wave heights and periods during the passages of four representative typhoons are compared with measured data from field wave stations on both east and west coasts. The results have shown that waves due to typhoons of paths 2, 3 and 4 can be reasonably simulated on east coastal waters. However, discrepancies increase for the simulated results on west coastal waters because the islands central mountains partly damage the cyclonic structures of the passing-over typhoons. It is also found that the included nested grid scheme in SWAN could improve the accuracy of simulations in coastal waters to facilitate further engineering practices.

A parabolic equation extended to account for rapidly varying topography

Abstract In this paper, following the procedure outlined by Li (1994. An evolution equation for water waves. Coastal Engineering, 23, 227-242) and Hsu and Wen (2000. A study of using parabolic model to describe wave breaking and wide-angle wave incidence. Journal of the Chinese Institute of Engineers, 23(4), 515–527) and Hsu and Wen (2000) the extended refraction–diffraction equation is recasted into a time-dependent parabolic equation. This model, which includes higher-order bottom effect terms, is extended to account for a rapidly varying topography and wave energy dissipation in the surf zone. The importance of the higher-order bottom effect terms is examined in terms of the relative water depth. The present model was tested for wave reflection in a number of different environments, namely from a plane slope with different inclinations, from a patch of periodic ripples. The model was also tested for wave height distribution around a circular shoal and wave breaking on a barred beach. The comparison of predictions with other numerical models and experimental data show that the validity of the present model for describing wave propagation over a rapidly varying seabed is satisfactory.

On the prediction of beach changes by a new 2-D empirical eigenfunction model

Abstract A new two-dimensional (2-D) empirical eigenfunction model is developed for the prediction of beach changes due to cross-shore and longshore sediment transports. Beach profile data, measured every two months along six segmented detached breakwaters, were analyzed to generate spatial and temporal orthogonal eigenfunctions. The temporal eigenfunctions are predicted through the use of the Markov process and a linear regression method as a time series to forecast changes in the sea bottom. This model simplifies the complex representation of eigenfunctions presented by Hsu et al. (1986), and takes advantage of this simplication to reduce artificial errors and save computer time for further applications. The predictability of the proposed model is examined through field observations as well as predictions of existing empirical eigenfunction models. The result shows that this 2-D empirical eigenfunction model is efficient and advisable for the prediction of the variability of beach changes around coastal structures.

Geometric characteristics of storm-beach profiles caused by inclined waves

A theoretical analysis shows that the geometric characteristics of a storm-beach profile is governed by a modified Iribarren number which includes the effects among the factors of beach slope, breaking wave angle and wave steepness. A series of experiments have been conducted in a three-dimensional movable bed model on the conditions of two different beach slopes and two incident wave angles as well as several erosive wave steepnesses. Based on the experimental data, the relative importance of each factor involved in the parameter is discussed. The empirical relationships between the geometric characteristics of a storm-beach profile and the modified Iribarren number are proposed through regression analysis.

A two-phase flow model of wave-induced sheet flow

This paper presents a two-phase flow model that simulates the fluid and sediment motions in the sheet flow region under oscillatory conditions. Some major forcing terms such as the fluid/particle and particle/particle interactions and turbulent stresses are included in the model. By improving some assumptions of most existing models, the present model specifies the equivalent sand roughness and bed concentration as a function of the Shields parameter, which is variable with time and is physically more realistic over a mobile flat bed. A wave friction factor, which is governed by a new parameter, is obtained from the present model formulation. The present model is shown to provide a more accurate estimate of sediment concentrations than those models using a constant equivalent sand roughness. Numerical analyses also show that the suspended sediment retards the mean velocity and suppresses turbulence.

The RIDE model: an enhanced computer program for wave transformation

Abstract A wave transformation model (RIDE) was enhanced to include the process of wave breaking energy dissipation in addition to water wave refraction, diffraction, reflection, shoaling, bottom friction, and harbor resonance. The Gaussian Elimination with partial Pivoting (GEP) method for a banded matrix equation and a newly developed bookkeeping procedure were used to solve the elliptic equation. Because the bookkeeping procedure changes the large computer memory requirements into a large hard-disk-size requirement with a minimum number of disk I/O, the simple and robust GEP method can be used in personal computers to handle realistic applications. The computing time is roughly proportional to N 1.7 , where N is the number of grid points in the computing domain. Because the GEP method is capable of solving many wave conditions together (limited by having the same wave period, no bottom friction and no breaking), this model is very efficient compared to iteration methods when simulating some of the wave transformation process.

A two-point method for estimating wave reflection over a sloping beach

Abstract This work presents a frequency-domain method for estimating incident and reflected waves when normally incident waves’ propagating over a sloping beach in a wave flume is considered. Linear wave shoaling is applied to determine changes of the wave amplitude and phase due to variations of the bathymetry. The wave reflection coefficient is estimated using wave heights measured at two fixed wave gauges with a distance. The present model demonstrates a high capacity of estimating reflection and shoaling coefficients from synthetic wave-amplitude data. Sensitivity tests for the present model due to measurement errors of wave amplitudes and distance of two probes can more accurately predict the reflection coefficients. The measurement error of wave amplitude affects more significantly than measurement error of distance of two probes on calculating reflection coefficient of waves over a sloping bed.

A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom

In this paper a complementary mild-slope equation (CMSE) is derived in order to investigate the transformation of progressive waves obliquely propagating over the sloping bottom more realistically. We introduce a new depth function which includes the wave refraction and the influence of the bottom slope α, perturbed to the second-order in the integral equation. A new depth-integrated mild-slope equation is derived, by using the above mentioned depth function, to model a time-harmonic motion of small amplitude waves in varying water depth. The simulated results reveal that the proposed model provides a significant improvement in the calculation of the wavenumber and the group velocity at different bottom slopes. With the increasing bottom slope, the discrepancies in the reflection coefficient of Bragg scattering between the analytical solution and the one calculated from the conventional mild-slope equation (MSE) and the modified MSE (MMSE) are seen to steadily increase. The group velocity of the waves, wh...

Extended time-dependent mild-slope and wave-action equations for wave–bottom and wave–current interactions

Extended mild-slope (MS) and wave-action equations (WAEs) are derived by taking into account high-order derivatives of the bottom profile and the depth-averaged current that were previously neglected. As a first step for this derivation, a time-dependent MS-type equation in the presence of ambient currents that consists of these high-order components is constructed. This mild-slope equation is used as a basis to form a wave-action balance equation that retains high-order refraction and diffraction terms of varying depths and currents. The derivation accurately accounts for the effects of the currents on the Doppler shift. This results in an ‘effective’ intrinsic frequency and wavenumber that differ from the ones of wave ray theory. Finally, the new WAE is derived for the phase-averaged frequency-direction spectrum in order to allow its use in stochastic wave-forecasting models.

Modulational Instabilities and Breaking Strength for Deep-Water Wave Groups

Progressionofnonlinear wave groups to breakingwasstudiednumericallyand experimentally. Evolution ofsuchwavegroupparametersasafunctionofdistancetobreakingandmodulationdepth—theheightratio of the highest and the lowest waves in the group—was described. Numerical model results demonstrated good agreement with experimental results in describing the behavior of the distance to breaking and modulation depth as functions of initial wave steepness. It was shown that energy loss appears to be a function of the modulation depth at the breaking onset. Energy loss grows with modulation depth up to a certain threshold of the latter. It was also shown that breaking probability for wave groups with modulation depth below 2.2 is very low.