Xiaozhou Ma

Laboratory observations of wave evolution, modulation and blocking due to spatially varying opposing currents

The nonlinear evolution of waves propagating on a spatially varying opposing current has been observed in a wave-current flume. Regular waves with different initial periods and different initial steepness, s (0.05 < s < 0.19), were generated and observed. Frequency downshift, even with very small initial steepness, was identified. As expected, it was found that opposing currents can have significant interactions with wavetrains. The ultimate frequency downshift increases with the increase in initial steepness. The evolution of frequency modulation was observed via the instantaneous frequency extracted by the Morlet-wavelet transform. The instantaneous frequency showed that often the process of frequency downshift can be local in time and gradual, but abrupt changes of local frequency were also detected. The presence of an opposing current can gradually block the primary wave energy and destroy the conservation of the wave action at downwave locations, thus increasing the asymmetric modulation and accelerating the effective frequency downshift.

Extreme waves generated by modulational instability on adverse currents

Physical experiments focusing on the propagation of gravity waves of finite depth on adverse currents were implemented to examine their effect on the development of the modulational instability and to study the geometric characteristics of extreme waves. A series of wave trains with varying initial steepness, perturbation frequency, and initial perturbed strength were mechanically generated in a wave-current flume. The present results show that opposing currents can speed the growth of the modulational instability, verifying the previous theory qualitatively. A current-modified nonlinear Schrodinger equation can predict the measured sideband growth rates well for wave trains with lower perturbation frequencies, but overestimated those with higher perturbation frequencies. On the other hand, the limiting steepness of extreme waves measured in the presence of opposing currents was smaller than that measured in quiescent water. Additionally, current strength was found to have limited influence on the geometr...

Numerical study of transient harbor resonance induced by solitary waves

The main purpose of this article is to decompose the response amplitudes of different resonant modes and to further study the wave energy distributions systematically inside long and narrow rectangular harbors with different bottom slopes when harbor oscillations are induced by normal-incident solitary waves. A series of numerical experiments are carried out using the FUNWAVE 2.0 model. The analysis procedure is mainly based on the improved normal mode decomposition method. Results show that when the incident wave height is small, the resonant wave energy inside harbors is dominated by the lowest few modes, and the higher modes only possess a very small proportion of the resonant energy; when the incident wave height increases, the relative energy distribution becomes uniform, and the proportion of energy in the higher modes increases. In addition, for the same incident wave height, the change of the bottom slope inside the harbor has a negligible effect on the relative energy distribution within the ranges of the variation in bottom slopes and the incident wave heights studied in this article.

Improvements on the normal mode decomposition method used in harbor resonance

In the article by Sobey (Rodney J. Sobey, 2006. Normal mode decomposition for identification of storm tide and tsunami hazard. Coastal Engineering 53, 289–301), the author proposed a normal mode decomposition method to calculate the eigenfrequencies, the eigenmodes and the response amplitudes of different resonant modes in natural harbors that are subjected to storm tides and tsunamis. However, the numerical method to address the no-flow boundary condition in that article is imprecise, which would lead to inexact eigenfrequencies and eigenmodes. In this article, the mirror-image method was proposed to improve this handling process. The accuracy of the improved normal mode decomposition method was verified using three verification tests. With a set of numerical experiments, it was determined that during the process of decomposing the response amplitudes of different resonant modes, the numerical fitting error between the simulated free surfaces and the corresponding fitted ones gradually increases with the wave nonlinearity inside the harbor. This article sought to identify the critical wave condition under which the normal mode decomposition method can accurately decompose the response amplitudes of different modes.

VARIATIONS OF STATISTICS FOR RANDOM WAVES PROPAGATING OVER A BAR

A series of physical experiments were conducted on the variations of statistics (skewness, kurtosis, groupiness) in random waves propagating over a submerged symmetrical bar. Random waves were generated using JONSWAP spectra while varying initial spectral width, wave height and peak frequency. It was found that the initial spectral width has a negligible effect on the variations of these statistical parameters. An abrupt change in wave groupiness is caused by wave breaking. Variations in the skewness and kurtosis mainly depend on the local water depth and wave height and period. Furthermore, the relationship between the skewness and kurtosis in the shoaling region is well predicted by the formula of Mori and Kobayashi (1998), but on the crest of the bar, the formula should be adjusted. Additionally, extreme waves that satisfy the definition of freak waves can be formed in the shoaling region close to the top of the bar. The probability occurrence of the freak waves has a negligible relationship with the initial spectral width, but the appearance of the extreme waves encounters with the increase of groupiness.

Spectra Evolution of Single Wave Packets in Finite Water Depth

A series of physical experiments were conducted to investigate the spectra evolution of single wave packets. Chirped-typed wave groups were selected in this study. Nine wave packets varying initial amplitudes and wave components were generated in the wave flume. Hence both non-breaking and breaking wave groups can be performed. It is found that the evolution process is far more than the linear superposition, and that it experiences significant nonlinear process. The modulational instability is found in the evolution of wave groups. For non-breaking groups, it is found that the most non-breaking energy dissipation occurs in the vicinity of the spectral peak (f/fp = 0.9–1.1). The non-breaking dissipation energy for spectral peak depends on depend on BFI (Benjamin-Feir Index). For breaking cases, the energy level of the above-peak frequency region (f/fp = 1.1–2.0) first increase slightly, and decrease during breaking occurring, but the overall change is limited. However, the below-peak frequency region (f/fp = 0.5–0.9) gains with the expense energy of the peak and above-peak frequency regions and the growth depends on the initial spectra width.Copyright

An analytical model of a typhoon wind field based on spiral trajectory

In typhoon risk assessment and warning, a critical component is a good representation of the typhoon wind field model. In this study, a new analytical model based on the logarithmic spiral trajectory model is developed to simulate the surface wind speed distribution of a typhoon. The logarithmic spiral trajectory model could overcome the limitation of the parametric gradient wind model. A slab surface layer of constant depth is used to solving the tangential equilibrium equation, and the frictional drag at the upper boundary of the surface layer is considered correctly. Consequently, the theoretical method for determining the Holland β parameter is derived from the logarithmic spiral trajectory model. It is concluded that β increases with the surface layer depth or decreases with the radius to maximum winds. By analyzing the change in kinetic energy of the air particle, the interpretation of the relationship between β and the influencing factors is provided. The models are applied to the 17th typhoon NESAT and the 19th typhoon NALGAE of 2011. Through comparisons between the observed wind records and the simulation results, the logarithmic spiral trajectory model proposed in this study could accurately simulate the wind speeds.

Numerical analysis of the nonlinear parameterization of waves in currents over a submerged sill with a non-hydrostatic model

An investigation of the effects of a uniform current strength direction (following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH, a non-hydrostatic numerical wave model. The nonlinear parameters (i.e., asymmetry, skewness, and kurtosis) are calculated, and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured. In the shoaling area of the submerged sill, the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction. Whereas nonlinear parameters grow with the strengthening of the following currents over the crest, they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.

Quantitative Calculation of Resonant Modes in Harbors Induced by Solitary Waves

The response amplitudes of resonant modes in harbors with different bathymetry induced by solitary waves with different wave heights are calculated using the Normal Mode Decomposition (NMD) method. Wave conditions inside harbors are simulated with a set of fully nonlinear Boussinesq equations. It is found that the resonant energy is dominated by the first few modes and the higher modes only possess a very small proportion of the total wave energy when the initial wave heights of incident solitary waves are relatively small. However, when the incident wave heights increase, the relative energy distribution of different resonant modes inside harbors becomes uniform and the proportion of energy in the higher modes increases.Copyright

Hydrodynamic Characteristics of Floating Pipes in Random Waves

The hydrodynamic performance characteristics of a round floating pipe model moored to the flume floor with pre-tensioned moorings has been investigated in random waves through an experimental program. The details of the models, set-up, experimental procedure and analysis of results are presented and discussed. The drag coefficient of floating pipes in random waves are analyzed. The motion responses, as well as the variations in the forces on the seaside mooring lines, are presented. In addition, statistical analysis has been carried out to prove that the heave and surge motions, as well as the peak mooring forces, follow the Rayleigh distribution.Copyright