Numerical modeling of long waves in shallow water using Incremental Differential Quadrature Method

Incremental Differential Quadrature Method (IDQM) as a rapid and accurate method for numerical simulation of Nonlinear Shallow Water (NLSW) waves is employed. To the best of authors’ knowledge, this is the first endeavor to exploit DQM in coastal hydraulics. The one-dimensional NLSW equations and related boundary conditions are discretized in space and temporal directions by DQM rules and the resulting system of equations are used to compute the state variables in the entire computational domain. It was found that the splitting of total simulation time into a number of smaller time increments, could significantly enhance the performance of the proposed method. Furthermore, results of this study show two main advantages for IDQM compared with other conventional methods, namely; unconditional stability and minimal computational effort. Indeed, using IDQM, one can use a few grid points (in spatial or time direction) without imposing any stability condition on the time step to obtain an accurate convergent solution.     

Modelling linear wave transformation induced by dissipative structures—Random waves

The relevant theory is presented and numerical results are compared with the analytical solution for the interaction of non-breaking waves with an array of vertical porous circular cylinders on a horizontal bed. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. The influence of the mechanical properties of porous structures and wave irregularity on wave transformation is analysed. Results for unidirectional and multidirectional wave spectra are compared to those obtained for regular waves. The model presented reproduces well the analytical results and provides a tool for analysing several engineering problems.     

Lagrangian measurements in the Kamchatka Current and Oyashio

From 1988 to 1993, 23 satellite-tracked drifting buoys entered the Kamchatka Current. The buoy trajectories showed a well-formed, high-speed current that originated near Shirshov Ridge, and flowed southward through Kamchatka Strait. During some years, the buoys turned eastward at 50°N, while in other years they were transported as far south as Japan (40°N). Only one buoy entered the Sea of Okhotsk. Eddies were evident in many of the buoy trajectories. Greatest maximum daily velocities (>100 cm s^–1) were observed south of Kamchatka Strait, with 50–60 cm s^–1 being more common.     

Caught in the act: the 20 December 2001 gravity flow event in Monterey Canyon

A sediment gravity flow descended through the axis of Monterey Canyon on 20 December 2001 at 13:35 Pacific standard time. The timing of this event is documented by a current-meter package which recorded an 11.9-dbar pressure increase in less than 10 min and was found 550 m down-canyon from its deployment site, buried completely within a >70-cm-thick gravity flow deposit. This event is believed to have started in less than 290 m of water because an instrument at this location was also lost at the same time. A 178-cm core collected after the event from the axis of the canyon at 1,297-m water depth contained fresh, greenish, chlorophyll-rich organic material at 32-cm sub-bottom depth, suggesting the event extended to this water depth. The only trigger identified for this mass movement event appears to be moderate sea and surf conditions. Thus, gravity flow events of this magnitude do not require an exceptional triggering event.     

Caught in the act: the 20 December 2001 gravity flow event in Monterey Canyon

A sediment gravity flow descended through the axis of Monterey Canyon on 20 December 2001 at 13:35 Pacific standard time. The timing of this event is documented by a current-meter package which recorded an 11.9-dbar pressure increase in less than 10 min and was found 550 m down-canyon from its deployment site, buried completely within a >70-cm-thick gravity flow deposit. This event is believed to have started in less than 290 m of water because an instrument at this location was also lost at the same time. A 178-cm core collected after the event from the axis of the canyon at 1,297-m water depth contained fresh, greenish, chlorophyll-rich organic material at 32-cm sub-bottom depth, suggesting the event extended to this water depth. The only trigger identified for this mass movement event appears to be moderate sea and surf conditions. Thus, gravity flow events of this magnitude do not require an exceptional triggering event.     

Boussinesq-type modelling using an unstructured finite element technique

A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model.