Tests and applications of an approach to absorbing reflected waves towards incident boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

Numerical Simulated Study on the Separation of Oblique Incident and Reflected Waves

The Goda's method of separating the frequency spectrum of the unidirectional incident and reflected waves is improved. The proposed method can be applied to the separation of oblique incident and reflected waves and the two wave gauges can be arranged in an arbitrary angle in front of a structure. When the projected distance of the two probes on the incident wave direction is the multiple ofthe half length of the incident waves, the singular problem will emerge by using the method. It is advised that when the projected distance of the two measured points on the incident wave direction is 0.05～0.45 times the wave length of peak frequency wave, good results can be obtained. The simulated resultant waves are separated by the method of numerical simulation and the separated wave spectra are basically corresponding to the target spectra input. The wave trains calculated by the separated incident and reflected wave frequency spectrum are approximated to the input wave trains and the reflected coefficient can be derived correctly. Therefore, the method proposed in this paper is reliable.     

Estimating Directional Distribution for Co-Existent Field of Incident and Reflected Waves

In the nearshore,the wave field contains reflected and incident waves in which there iscorrelation between their phases due to the effect of reflection by some obstacles.Based on the extendedeigenvector method(EEV)derived by Guan et al.,a modified method(MEEV)is proposed as a generaland practical approach to estimating directional spectra for the co-existent field of incident and reflectedwaves and a formula is given for direct calculation of the reflection coefficient.The results of numericalsimulations show that MEEV is superior to EEV in resolution power,and the computed reflectioncoefficient agrees well with the real value within a certain range of incident angle.     

Numerical Modelling of Standing Waves with Three-Dimensional Non-Linear Wave Propagation Model

Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, .and the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions     

Analysis of Directional Spectra and Reflection Coefficients in Incident and Reflected Wave Field

In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.     

Simulation of Bay of Bengal Tropical Cyclones with WRF Model: Impact of Initial and Boundary Conditions

An attempt is made to delineate the relative performances and credentials of GFS, FNL, and NCMRWF global analyses/forecast products as initial and boundary conditions (IBCs) to the WRF-ARW model in the simulation of four Bay of Bengal tropical cyclones (TCs). The results suggest that FNL could simulate horizontal advection of vorticity maxima at 850 hPa; hence, the tracks are more realistic with least errors as compared to GFS and NCMRWF. The mean landfall errors for 24-, 48-, and 72-hour forecasts are 73, 41, and 72 km, respectively. The TC intensity is well captured by NCMRWF IBCs, as it could predict 850 hPa vorticity maxima. The 24-hour accumulated rainfall is well simulated with FNL, and equitable threat score is more than 0.2 up to 100 mm with minimum bias.     

Transient response of harbours to long waves under resonance conditions

This paper presents the results of a study aimed at quantifying the time–response of harbour basins to long waves under resonance conditions. On the basis of numerical simulations reproducing long waves in the yacht harbour of Rome (Ostia, Italy), it shows that the results valid for periodic forcing waves, acting for an infinitely long time, as those provided by models based on elliptic equations like the Helmoltz and the mild-slope equations, can be misleading with respect to the more realistic ones that can be obtained using time-varying wave equations. Taking advantage of the similarity between the processes studied here and a simple one-dimensional resonator, a method is also proposed to roughly estimate a time–response parameter of each mode of the harbour, using results from steady-state numerical model results, commonly applied for studying harbour resonance in engineering practice. On the basis of further numerical simulations, aimed at reproducing schematic harbour layouts, the effect on resonance of the position of the entrance and of an outer harbour is studied. The results indicate that the effects of design solutions to reduce resonance, by placing the entrance at the middle of the harbour, or using the outer harbour as a resonator, can be correctly evaluated only when considering the time needed for the oscillations to fully develop.     

Transformation of the Indonesian Throughflow Water by Vertical Mixing and Its Relation to Tidally Generated Internal Waves

Numerical experiments with two-dimensional nonhydrostatic model have been performed to investigate tidally generated internal waves at the Dewakang sill at the southern Makassar Strait where two large-amplitude “bumps” of relatively shallow water exist. We investigate the effect of these features on vertical mixing, with emphasis on the transformation of the Indonesian throughflow (ITF) water properties. The result shows that large-amplitude internal waves are generated at both bumps by the predominant M₂ tidal flow, even though the condition of the critical Froude number and the critical slope are not satisfied. The internal waves induce such vigorous vertical mixing in the sill region that the vertical diffusivity attains a maximum value of 6 × 10⁻³ m²s⁻¹ and the salinity maximum and minimum core layers characterizing the ITF thermocline water are considerably weakened. Close examination reveals that bottom-intensified currents produced mainly by the joint effect of barotropic M₂ flow and internal tides generated in the concave region surrounding both bumps can excite unsteady lee waves (Nakamura et al., 2000) on the inside slopes of the bumps, which tend to be trapped at the generation region and grow into large-amplitude waves. Such generation of unsteady lee waves does not occur in case of one bump alone. Trapping and amplification of the waves in the sill region induce large vertical displacements (∼60 m) of water parcels during one tidal period, leading to strong vertical mixing there. Since the K₁ tidal currents are relatively weak, large-amplitude internal waves causing intense vertical mixing are not generated. This revised version was published online in July 2006 with corrections to the Cover Date.     

An assessment model for the fate and environmental effects of offshore drilling mud discharges

The benthic boundary layer transport (bblt) model was developed to assess potential impact zones from drilling mud discharges from offshore oil and gas drilling. The model focuses on the drift, dispersion and concentration levels of the suspended fraction of the drilling mud fines in the benthic boundary layer with the assumption of a spatially homogeneous environment. The current version of the model includes a wave boundary layer, a breakup module for drilling mud flocs, a dose–response module for scallops, and a graphical user interface (GUI). The GUI was written in Java which makes the code largely platform independent. Simulations of suspended barite concentration near Sable Island on the Scotian Shelf during drilling in the fall of 1999 reproduce the very low concentrations (generally less than 1 μg L⁻¹) observed during the Environmental Effects Monitoring program. However, the simulations also exhibited concentrations in excess of the no-effects concentration for scallops (100 μg L⁻¹) prior to the sampling program. The model estimates that the potential impact on scallops in the vicinity of the drilling is a few days of lost growth over scales of a few kilometers.