The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

This paper presents specific features of solitary wave dynamics within the framework of the Ostrovsky equation with variable coefficients in relation to surface and internal waves in a rotating ocean with a variable bottom topography. For solitary waves moving toward the beach, the terminal decay caused by the rotation effect can be suppressed by the shoaling effect. Two basic examples of a bottom profile are analyzed in detail and supported by direct numerical modeling. One of them is a constant‐slope bottom and the other is a specific bottom profile providing a constant amplitude solitary wave. Estimates with real oceanic parameters show that the predicted effects of stable soliton dynamics in a coastal zone can occur, in particular, for internal waves.     

Numerical grids used in a coastal ocean model with breaking wave effects

In coastal ocean modeling, traditional single-block rectangular (Cartesian) grids have been most commonly used for their simplicity. In many cases, these grids may be not well suited (even at very high resolutions) for regions with complicated physical fields, open boundaries, coastlines, and bottom bathymetry. The numerical curvilinear nearly orthogonal/orthogonal, single/multi-block coastline-following grids for the Mediterranean Sea, Monterey Bay and the South China Sea (SCS) are presented. These grids can be used in coastal ocean modeling to enhance model numerical solutions and save computer resources by giving better treatment of regions with high gradients such as areas of complicated coastlines and steep slopes of shelf breaks, complicated bottom topography, open boundaries, and multi-scale physical phenomenon. Grid generation techniques are used to designed these grids. This kind of grids can also easily increase horizontal resolutions in the subregion of the model domain, without increasing the computational expense, with a higher resolution over the entire domain.A three dimensional coastal ocean model with breaking wave effects is also presented and applied. The ocean system is a primitive equation modeling system with grid generation routines and a turbulent closure which is capable of taking surface breaking wave effects into account. The system also includes a grid package which allows model numerical grids to be coupled with the ocean model. The model code is written for multi-block grids, but a single-block grid is used for the South China Sea (SCS). The model with breaking wave effects and a grid of 121 × 121 grid points are used to simulate the winter circulation of the SCS as an example. The model output of the 60-day run shows the observed upwelling locations in the sea surface salinity field.     

Generation and dissipation of ocean surface waves

Ocean surface waves constitute one of the most important sources of external forces that act on ships and offshore structures. Most ocean waves are generated by wind, but various other effects such as currents, ground and coastal topology, breaking and wave–wave interaction have an influence on the growth and dissipation of wave energy at specific frequency ranges. These water waves are inherently random in nature and their exact shape is difficult to describe, even when confining the described area to a small range. While many different approaches exist to describe the spectral characteristics of ocean waves, some of the processes which affect the generation of waves are still poorly understood. This paper addresses some techniques which serve to describe seaway spectra with respect to the subsequent analysis of dynamic mechanical systems in the ocean such as ships, platforms and pipelines. Advantages and limits of the different approaches are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Wave Equations for Oceanic Internal Solitary Waves

In the coastal ocean, the interaction of barotropic tidal currents with topographic features such as the continental shelf, sills in narrow straits, and bottom ridges are often observed to generate large amplitude, horizontally propagating internal solitary waves. These are long nonlinear waves and hence can be modeled by equations of the Korteweg–de Vries type. Typically they occur in regions of variable bottom topography, with the consequence that the appropriate nonlinear evolution equation has variable coefficients. Further, as these waves can be long‐lived it is necessary to take account of the effects of the Earth's background rotation. We review this family of model evolution equations and some of their pertinent solutions, obtained both asymptotically and numerically.     

THE USE OF TELESCOPING SPATIAL SCALES TO CAPTURE INSHORE TO SLOPE DYNAMICS IN MARINE ECOSYSTEM MODELING

Abstract Ecosystem processes function at many scales, and capturing these processes is a challenge for ecosystem models. Nevertheless, it is a necessary step for considering many management issues pertaining to shelf and coastal systems. In this paper, we explore one method of modeling large areas with a focus at a range of scales. We develop an ecosystem model that can be used for strategic management decision support by modeling the waters off southeastern Australia using a polygon telescoping approach, which incorporates fine‐scale detail at the coastal zone, increasing in scale to a very coarse scale in the offshore areas. This telescoping technique is a useful tool for incorporating a wide range of habitats at different scales into a single model.     

Numerical multi-block grids in coastal ocean circulation modeling

In coastal ocean modeling, one desires to capture the evolution and interaction of multi-scales of physical phenomena in a complicated physical domain. With limited computer resources, an appropriate choice of the numerical grid has a key role in determining the quality of the solution of a numerical coastal ocean model. Traditionally, single-block rectangular grids have been most commonly used in coastal ocean modeling for their simplicity. An effective coastal ocean model represents the dynamics of the coastal ocean flow on a numerical grid, including the effects of complicated features such as coastlines, bottom topography (submarine canyons, seamounts, narrow straits), and multi-scale physical phenomena. These problems require a model grid system more efficient than a traditional single-block rectangular grid. The model grids must give better resolution of coastlines and boundary conditions, multi-scale physical phenomenon, and save computer resources. These grids can also easily increase horizontal resolution in a subregion of the model domain without increasing computer expense with high resolution over the entire domain. The multi-block numerical generation grid technique is used in developing a coastal ocean system applied to the Mediterranean Sea (MED) with complicated coastlines, bottom topography and multi-scale physical features. The MED coastal ocean system consists of the MED model based on the Princeton Ocean Model, numerical grid generation routines, and a grid package which allows the model to be coupled with model grids. The traditional, nine-block orthogonal grid, and eight-block curvilinear nearly orthogonal coastline-following grid are used in the study. The numerical solutions with the three grids are compared in term of effectiveness. The numerical simulations show some MED basic physical features.     

Directional Spectra-Based Clustering for Visualizing Patterns of Ocean Waves and Winds

The energy distribution of wind-driven ocean waves is of great interest in marine science. Discovering the generating process of ocean waves is often challenging and the direction is the key for a better understanding. Typically, wave records are transformed into a directional spectrum which provides information about the wave energy distribution across different frequencies and directions. Here, we propose a new time series clustering method for a series of directional spectra to extract the spectral features of ocean waves and develop informative visualization tools to summarize identified wave clusters. We treat directional distributions as functional data of directions and construct a directional functional boxplot to display the main directional distribution of the wave energy within a cluster. We also trace back when these spectra were observed, and we present color-coded clusters on a calendar plot to show their temporal variability. For each identified wave cluster, we analyze wind speed and wind direction hourly to investigate the link between wind data and wave directional spectra. The performance of the proposed clustering method is evaluated by simulations and illustrated by a real-world dataset from the Red Sea. Supplementary materials for this article are available online.     

O?shore ?oating wind turbine and its dynamic problems?

Green energy sources and ocean wind power are plentiful in deep sea. More and more o?shore wind power plants are constructed in the deep water over hundred meters below the surface. While o?shore ?oating wind turbine system is working, wind turbine, ?oating foundation, and mooring system a?ect each other with wind, waves, and currents acting on them. Various o?shore ?oating wind turbine systems and the encoun-tered environmental loads are brie?y reviewed and discussed. It is di?cult and crucial to comprehensively analyze the aerodynamic-hydrodynamic-service system-structure un-der the coupling e?ect of o?shore ?oating wind turbine system. The environmental ?ow ?eld, structure scale, and rational applications of theories and approaches should be well considered in advance.     

On capture and acceleration of heavy ions (a-particle) in high-speed solar wind

The α-particles and other heavy ions, as well es a few protons are observed to be faster than the main part of protons by about the local Alfven speed in the high-speed solar wind. It is suggested that when the velocity of the solar wind is equal to the local Alfven velocity, another Iow-frequency kinetic Alfvan wave will be excitated, and trap ail the α-particles and a few protons, so these ions have a local Alfven velocity faster than the other parts of the solar wind. The undamping kinetic Alfven waves change into Iow-frequency Alfven solitons in the solar wind. This model can explain the observation and give the conditions of wave excitated and ions trapped.     

On capture and acceleration of heavy ions (α-particle) in high-speed solar wind

The α-particles and other heavy ions, as well as a few protons are observed to be faster than the main part of protons by about the local Alfven speed in the high-speed solar wind. It is suggested that when the velocity of the solar wind is equal to the local Alfven velocity, another low-frequency kinetic Alfven wave will be excitated, and trap all the α-particles and a few protons, so these ions have a local Alfven velocity faster than the other parts of the solar wind. The undamping kinetic Alfven waves change into low-frequency Alfven solitons in the solar wind. This model can explain the observation and give the conditions of wave excitated and ions trapped.     

CONTINGENT VALUATION OF MARINE PROTECTED AREAS: SOUTHERN CALIFORNIA ROCKY INTERTIDAL ECOSYSTEMS

ABSTRACT. Designation as Marine Protected Areas (MPAs) can protect coastal ecosystems, but apparently has not effectively protected the rocky intertidal zone in urban Southern California. Here, illegal collecting and habitat disturbance harm coastal marine life. We surveyed day visitors to sandy beaches or adjacent rocky habitats in Orange County. Using the close‐ended, double‐bounded contingent valuation method, we estimate the benefit of more effective enforcement and management of MPAs designed to avoid coastal ecosystem decay. We solve the problem of sample selection bias, introduced by the likelihood that the sample disproportionately includes respondents who visit more frequently and who may have a higher willingness to pay (WTP). We estimate the WTP for enacting policies to reduce illegal collecting and on‐site habitat disturbance to average $6 per family‐visit. Our estimate is consistent with other studies that estimate consumer surplus at $15 per person‐trip for nearby, lower quality beaches, and extrapolates from other studies to $3.6 $4.8 million per mile of coastline.     

The Evolution of Internal Undular Bores over a Slope in the Presence of Rotation

The large‐amplitude internal waves commonly observed in the coastal ocean often take the form of unsteady undular bores. Hence, here, we examine the long‐time combined effect of variable topography and background rotation on the propagation of internal undular bores, using the framework of a variable‐coefficient Ostrovsky equation. Because the leading waves in an internal undular bore are close to solitary waves, we first examine the evolution of a single solitary wave. Then, we consider an internal undular bore, for which two methods of generation are used. One method is the matured undular bore developed from an initial shock box in the Korteweg–de Vries equation, that is the Ostrovsky equation with the rotational term omitted, and the other method is a modulated cnoidal wave solution of the same Korteweg–de Vries equation. It transpires that in the long‐time model simulations, the rotational effect disintegrates the nonlinear waves into inertia‐gravity waves, and then there emerge complicated interactions between these inertia‐gravity waves and the modulated periodic waves of the undular bore, especially at the rear part of the undular bore. However, near the front of the undular bore, nonlinear effects further modulate these waves, with the eventual emergence of nonlinear envelope wave packets.     

Analytic models for West Coast storm surges,with application to events of January 1976

Simple mathematical models describing wind-induced motion on a continental shelf are used to predict storm surges at the port of Milford Haven on the west coast of the British Isles. Attention is concentrated on surge events occurring during the stormy month of January 1976. It is demonstrated that useful first-order accuracies in prediction can be achieved. Oceanic influence on the coastal surge is shown to be small. Satisfactory results are obtained with wind input data coming either from the analysis of daily weather charts or from recorded values of wind speed and direction at a group of meteorological stations.     

Nonlinear amplification of ocean waves in straits

Theoretical and Mathematical Physics - Using the exact Hasselmann equation, we study wind-driven deep-water ocean waves in a strait with the wind directed orthogonally to the shore. The strait has...     

Simulating wave transmission in the lee of a breakwater in spectral models due to overtopping

Spectral wave models have experienced constant development and vast improvements over the past decades. They are constantly being extended and refined in order to cover the complex wave transformation processes that take place in the coastal zone. Nevertheless, wave transmission due to overtopping has not been treated similarly yet. In this paper, a methodology to include wave generation due to overtopping in spectral wave models is presented. Incorporation of overtopping aims at better simulating the wave disturbance in the lee side of a system of offshore breakwaters and the induced hydrodynamic processes. So far, the waves generated due to wave overtopping were being neglected. The methodology consists of executing sequential simulations at small time step intervals and whenever wave overtopping occurs in a breakwater, waves are generated and transmitted in the lee side of the structure. This is achieved by modifying the boundary condition at the lee of a coastal structure to account for wave generation due to overtopping. Additionally, the transmitted spectrum source function was modified, to capture the observed transfer of energy in the higher frequencies of the spectrum due to the aforementioned overtopping process. The above methodology was implemented in the open source wave model TOMAWAC and verification with experimental measurements was carried out yielding satisfactory results. Inclusion of wave transmission due to overtopping in spectral wave models is considered to be a valuable asset, especially for the simulation of inshore hydrodynamic processes.     

Existence and qualitative theory for stratified solitary water waves

This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water and vacuum is a free boundary where the pressure is constant. We prove that, for any smooth choice of upstream velocity field and density function, there exists a continuous curve of such solutions that includes large-amplitude surface waves. Furthermore, following this solution curve, one encounters waves that come arbitrarily close to possessing points of horizontal stagnation.We also provide a number of results characterizing the qualitative features of solitary stratified waves. In part, these include bounds on the wave speed from above and below, some of which are new even for constant density flow; an a priori bound on the velocity field and lower bound on the pressure; a proof of the nonexistence of monotone bores in this physical regime; and a theorem ensuring that all supercritical solitary waves of elevation have an axis of even symmetry.     

Modeling aspects and numerical analysis of offshore systems

There is a strong effort to improve the efficiency of renewable energy systems in order to reduce the CO₂ emissions. This paper addresses an approach to increase the efficiency of an ocean wave energy plant with a model based predictive controller. For this controller it is necessary to have a prediction of the ocean waves and a model of the whole system. The future development of the ocean waves is predicted by an AR-model. A system identification yields the model of the energy plant. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling the coastal ocean over a time period of several weeks

From a scale analysis of hydrodynamic phenomena having a significant action on the drift of an object in coastal ocean waters, we deduce equations modeling the associated hydrodynamic fields over a time period of several weeks. These models are essentially non linear hyperbolic systems of PDE involving a small parameter. Then from the models we extract a simplified and nevertheless typical one for which we prove that its classical solution exists on a time interval which is independent of the small parameter. We then show that the solution weak-∗ converges as the small parameter goes to zero and we characterize the equation satisfied by the weak-∗ limit.     

Scattering of an incident acoustic wave by an elastic sphere in a shallow water

The scattering of acoustic waves by an elastic sphere in a shallow ocean wave guide is investigated taking into account the shear waves which can exist in addition to compressional waves in scatterers of solid material. Expressions for the scattered waves are given. Numerical values for a quantity called the farfield form function for various depth are presented in graphical forms.