Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region

An improvement on the simulation of outgoing waves on a time dependent numerical model for water wave propagation in the nearshore region is presented. The governing equations consist of a system of first order partial differential equations (PDEs), the equation of continuity and the equation of motion. A comparative study of first order radiation boundary conditions (BCs) and first order radiation BCs combined with sponge layers is presented for cases where outgoing waves leave the numerical domain of calculation through the open boundary. A reduction of spurious reflections from the numerical open boundaries can be obtained with an irrelevant increase in terms of computational cost.     

Open boundaries in short wave simulations — A new approach

A new way of implementing radiation boundary conditions in finite difference schemes is reported. Instead of prescribing the incident field at the model boundary, waves are generated inside the model boundary. All outgoing waves are absorbed at open boundaries using so-called “sponge” layers.     

Numerical implementation of the harmonic modified mild-slope equation

A numerical solver is presented of the modified time-independent mild-slope equation, which incorporates energy dissipation. Using a second-order parabolic approximation, the following external boundary conditions are modelled: open and fully transmitting to both incoming and outgoing waves; partially reflecting, and; fully absorbing. Discretisation of the governing equation and boundary conditions is by means of a second-order accurate central difference scheme. The resulting sparse-banded matrix is solved using an inexpensive banded solver with Gaussian elimination. The numerical predictions are in excellent agreement with the analytical solution for the interaction of non-breaking waves with an array of vertical surface-piercing circular cylinders on a horizontal bed. Results are compared with those for the same array on various seabed topographies. The model is robust and can be used for wave propagation in complex geometries. It has fewer restrictions associated with wave obliqueness at boundaries than traditional models based on the mild-slope equation.     

Three-dimensional numerical simulation of oblique wave action on vertical walls

1 Introduction A vertical wall is one of the typical maritime sheltering structures in the coastal region, which is mainly subjected to wave forces. It has been a com- mon engineering assumption adopted for design pur- poses that normally incident wave fo…     

Improved boundary equations for elliptic water wave models

Approximate equations for the elliptic mild slope equation are derived based on Padé approximation and used as absorbing boundaries. The new boundary equations can absorb the incident waves for high range of wave incidence angle. In addition, the new boundary equations can be used iteratively to refine the solution by eliminating reflections from the boundaries. An iterative conjugate gradient scheme has been used to solve the elliptic water wave equation and the new boundary equations. The model developed can accommodate for wave diffraction, refraction and reflections from structures with wide range of wave angles at the boundaries. The new model has been tested for several cases. The model compares very well with other models.     

Stationary states of a pair of tangent identical vortex spots in a barotropic ocean

The method for constructing limiting forms of steady states of vortex patches characterized by the presence of corners on the boundary is presented. The method is based on a continuation of the solution (the streamline which must coincide with the vortex boundary) when passing through the singular point to those part of the common vortex border whose tangent is continuous at the critical point. Limiting steady states of a pair of identical touching vortex patches are constructed for the cases of unlimited and circular barotropic oceans. It is found that, for the case of a circular ocean, the solution of maximum area is the domain bounded by two diameters intersecting at right angles. This conclusion is also valid for an unlimited ocean when the vortex pair of infinite area takes even/odd quadrants whose boundaries are formed by the asymptotes of solutions of finite area. The results add new members to the set of known exact analytical solutions of the problem of steady states of vortex patches.     

On the simulation of temperature and salinity fields in the Arctic Ocean

This paper considers the formation of the thermohaline structure of the Arctic Ocean: the formation of the salinity field and a freshwater reservoir in the Beaufort Sea and the transport of warm Atlantic water into the central part of the Arctic Ocean. A new version of the Finite Element Model of the Arctic Ocean (FEMAO) with a low spatial resolution is used. The main distinctions of this version are the following features: a new equation of state, a more sophisticated parameterization of vertical turbulence, modified formulations for the boundary conditions on open boundaries (using satellite data on the sea level) and at the upper boundary of the ocean, and the use of a variable eddy diffusivity in the parameterization of the eddy transport of a scalar. Our experiments indicated that the use of the parameterization of the eddy transport of a scalar enhances the transport of warm Atlantic waters to the central part of the Arctic Ocean through the Fram Strait; the results are most realistic when a variable coefficient is used. The Neptune effect has a contradictory role and, in the future, a higher spatial resolution should be used instead of this parameterization. We revealed that a key factor in the thermohaline fields on a large time scale is the interaction with the Atlantic Ocean, which is the source of heat and saline water.     

Assessment of open boundary conditions on the elliptic formulation of the mild-slope equation

The performance of open boundaries in a finite differences scheme of the elliptic mild-slope equation is assessed. The wave propagation results show that lowest order parabolic radiation boundary conditions, unlike sponge layers combined with first order radiation boundary conditions, are an efficient alternative to first order radiation boundary conditions in order to improve the accuracy of the numerical solution of the problem.     

Interactions of Mesoscale Eddy and Western Boundary Current: A Reduced-Gravity Numerical Model Study

A reduced-gravity primitive equation eddy resolving model is used to study the interaction of a typhoon-induced eddy and a wind-driven general circulation. A typhoon-induced eddy is characterized by a core with a relative vorticity of the same order as the local Coriolis parameter. This eddy is neutrally stable relative to a disturbance induced by the westward advection of the eddy, due to the planetary β-effect. Hence, its evolution in the open ocean is similar to the classical frontal geostrophic eddy. Within the western boundary flow regime, the eddy is entrained northward by the mean circulation. This northward eddy advection and the mean-vorticity advection due to eddy flow induce another disturbance with a north-south asymmetry into the circular eddy. Together with the zonal asymmetric disturbance, associated with the planetary β-effect, the original circular eddy becomes unstable. The nonlinear eddy-flow interactions in the eastern flank of a western boundary current causes the eddy to deform quickly into an ellipse and lose its waters and energy into the mean circulation.     

Modeling the sea currents in open basins: The case study for the Hawaiian Island region

The fields of currents in open basins are studied with the use of a mathematical model of ocean hydrodynamics. The area of the Hawaiian Islands is taken as an example. The model, based on three-dimensional equations of thermohydrodynamics, is solved for a domain with open boundaries, at which adaptive boundary conditions are set. We analyze the results of numerical experiments with given monthly mean climatic conditions at the ocean surface and open lateral boundaries with consideration for tides M ₂ and K ₁. A comparison of the model solutions and observational data shows that the model can realistically reproduce the mean parameters of the ocean state and their variability. The model solutions for the given area were found to have a northward current in the upper oceanic layer. This current clearly manifests itself in averaged fields. The characteristics of averaged currents indicate that the upper 100–150-m layer between the islands of Hawaii and Maui as well as between the islands of Molokai and Oahu is characterized by water transport from the west to the east side of the ridge of islands. The results obtained and the model proposed can be used to monitor physical fields of the ocean.     

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.     

On the use of current meter data to assess the realism of ocean model simulations

The evaluation of ocean simulations against observed datasets is essential to assess their realism and to guide model development, but often remains qualitative, and ignores certain datasets. This paper presents a three-dimensional, quantitative comparison of a 1/6° Atlantic numerical simulation (CLIPPER) with the WOCE current meter dataset in terms of mean velocity and eddy kinetic energy. Our metrics reveal the good behaviour of CLIPPER open boundary conditions and forcing with respect to full-depth current records. Due to its still moderate resolution, however, the model globally underestimates the observed mean speeds and eddy activity. This discrepancy is barely noticeable at low latitudes but increases toward the poles, probably since the poleward decrease of the Rossby radius exceeds that of the horizontal grid step. At least in this eddy-admitting regime, it is suggested that the numerics of geopotential-coordinate models like ours dissipate mean and eddy momentum at depth and adversely affect current–topography interactions.     

A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry

A consistent coupled-mode model recently developed by Athanassoulis and Belibassakis [1], is generalized in 2+1 dimensions and applied to the diffraction of small-amplitude water waves from localized three-dimensional scatterers lying over a parallel-contour bathymetry. The wave field is decomposed into an incident field, carrying out the effects of the background bathymetry, and a diffraction field, with forcing restricted on the surface of the localized scatterer(s). The vertical distribution of the wave potential is represented by a uniformly convergent local-mode series containing, except of the ususal propagating and evanescent modes, an additional mode, accounting for the sloping bottom boundary condition. By applying a variational principle, the problem is reduced to a coupled-mode system of differential equations in the horizontal space. To treat the unbounded domain, the Berenger perfectly matched layer model is optimized and used as an absorbing boundary condition. Computed results are compared with other simpler models and verified against experimental data. The inclusion of the sloping-bottom mode in the representation substantially accelerates its convergence, and thus, a few modes are enough to obtain accurately the wave potential and velocity up to and including the boundaries, even in steep bathymetry regions. The present method provides high-quality information concerning the pressure and the tangential velocity at the bottom, useful for the study of oscillating bottom boundary layer, sea-bed movement and sediment transport studies.     

Volume transport of the western boundary current penetrating into a marginal sea

The amount of penetration of a western boundary current into a marginal sea which is connected to an open ocean by two narrow straits is estimated from a linear, steady and barotropic theoretical model. In this model the western boundary current in the open ocean is driven by a wind stress imposed at the sea surface. The inflow of the water of the open ocean into the marginal sea is caused by the pressure difference between two straits produced by the wind-driven circulation in the open ocean.Main external parameters are combined into two non-dimensional parameters; and (the ratio of the depth of the marginal sea to that of the open ocean), whereb is the distance between north and south boundaries of the ocean,D ₀ is the depth of the open ocean, is the latitudinal variation of the Coriolis parameter andR is the coefficient of friction. The friction is assumed to be proportional to the flow velocity.In the limit of infinite the volume transport into the marginal sea is not affected by the width of two straits and . It is mainly controlled by the wind stress and the positions of two straits. For finite values of , however, the volume transport depends considerably on and the width of the straits.Guided by both this model and physical considerations, we obtained a relation between the volume transport into the marginal sea and the external parameters. This relation predicts that about 2 % of the volume transport of the Kuroshio penetrates into the Japan Sea.     

Large eddy simulation of stratified mixing in a three-dimensional lock-exchange system

Accurate and computationally-efficient modeling of stratified mixing processes are of paramount importance in both coastal and large-scale ocean circulation. In this study, our main objective is to investigate the feasibility and accuracy of large eddy simulation (LES) as a possible tool to study small-scale oceanic processes. To this end, LES is evaluated in a 3D lock-exchange problem, which contains shear-driven mixing, internal waves, interactions with boundaries and convective motions, while having a simple domain, initial and boundary conditions, and forcing.Two general classes of LES models are tested, namely eddy viscosity (EV) models based on constant–coefficient and dynamic Smagorinsky models, and an approximate deconvolution (AD) model. By noting that the dynamic Smagorinsky and AD models have different strengths in that the former is good in providing appropriate dissipation while the latter in preserving the detail of coherent structures on coarse resolution meshes, a hybrid approach combining EV and AD models is also evaluated. A direct numerical simulation (DNS) is performed as the benchmark solution, and all LES models are tested on three coarse meshes. The main measure of mixing is taken as the temporal evolution of background potential energy.It is found that constant-coefficient Smagorinsky models can only provide a marginal improvement over under-resolved simulations, while both dynamic Smagorinsky and AD models lead to significant improvements in mixing accuracy. The primary accomplishment of this study is that it is shown that the hybrid approach attains the best agreement with the mixing curve from DNS, while being computationally approximately a thousand times faster.     

Nonlinear dynamics of the circulation variability in the western ocean

The nonlinear dynamics of the low-frequency variability of a mid-latitude ocean are studied. The mechanism of the separation of the western boundary current from the western wall, as well as the meridional displacements of the separation point and the separated eastward jet, is analyzed. A regional barotropic quasigeostrophic eddy-resolving numerical model is used for the analysis. The flow in a rectangular domain is simulated by the constant inflow and outflow of fluid through the boundaries. A regime when the nonlinearity prevails over the dissipation and the advection and β terms are of the same order of magnitude is considered, which is characteristic of the actual ocean. When the nonlinearity exceeds the threshold value, a periodic solution is obtained. The solution is determined by the nonslip boundary condition at the western wall. The solution obtained is studied in detail. The meridional displacements of the western boundary current separation point with respect to the western wall and the separated eastward jet can reach a few hundred kilometers. Their intensities and the intensity of the recirculation gyre in the western boundary current are found to oscillate with a period of about five years.     

基于海洋调查实测资料的中尺度涡旋识别结果的验证及边界拟合技术

结合卫星高度计资料,本文在海洋中尺度涡旋综合识别法(综合法)的基础上,利用实测资料对识别的涡旋边界和中心点进行比对验证,得出以下结论:(1)通过诊断涡旋识别的边界切线与实测海流矢量的夹角,结果表明综合法识别的涡旋边界形态基本可以反映实测涡旋的水平形态;(2)利用实测海流和温度资料反演涡旋中心,通过与综合法识别的涡旋中心...     

Sound-pressure level calculations using the RRA algorithm fordepth-dependent speeds of sound valid at turning points and focal points

Sound-pressure level (SPL) calculations are made along individual ray paths for arbitrary, one-dimensional, depth-dependent speeds of sound using an enhanced version of the RRA (recursive ray acoustics) algorithm. The SPL calculations are valid (i.e., finite) at turning points and focal points and do not require the use of Airy functions. The SPL calculations include the effects of frequency-dependent volume attenuation and frequency-dependent attenuation due to surface and bottom reflections. The ocean surface and bottom are treated as boundaries between viscous fluid media. Although the ocean surface is modeled as a planar boundary, the bathymetry is an arbitrary function of horizontal range. Sound speed versus depth and bathymetric data are represented by orthogonal function expansions. Computer simulation results from preliminary test cases are presented     

Effects of mesoscale eddies on the internal solitary wave propagation

The mesoscale eddy and internal wave both are phenomena commonly observed in oceans. It is aimed to investigate how the presence of a mesoscale eddy in the ocean affects wave form deformation of the internal solitary wave propagation. An ocean eddy is produced by a quasi-geostrophic model in f-plane, and the one-dimensional nonlinear variable-coefficient extended Korteweg-de Vries (eKdV) equation is used to simulate an internal solitary wave passing through the mesoscale eddy field. The results suggest that the mode structures of the linear internal wave are modified due to the presence of the mesoscale eddy field. A cyclonic eddy and an anticyclonic eddy have different influences on the background environment of the internal solitary wave propagation. The existence of a mesoscale eddy field has almost no prominent impact on the propagation of a smallamplitude internal solitary wave only based on the first mode vertical structure, but the mesoscale eddy background field exerts a considerable influence on the solitary wave propagation if considering high-mode vertical structures. Furthermore, whether an internal solitary wave first passes through anticyclonic eddy or cyclonic eddy, the deformation of wave profiles is different. Many observations of solitary internal waves in the real oceans suggest the formation of the waves. Apart from topography effect, it is shown that the mesoscale eddy background field is also a considerable factor which influences the internal solitary wave propagation and deformation.     

The transition zone of the Canary Current upwelling region

Like all the major upwelling regions, the Canary Current is characterised by intense mesoscale structure in the transition zone between the cool, nutrient-rich waters of the coastal upwelling regime and the warmer, oligotrophic waters of the open ocean. The Canary Island archipelago, which straddles the transition, introduces a second source of variability by perturbing the general southwestward flow of both ocean currents and Trade winds. The combined effects of the flow disturbance and the eddying and meandering of the boundary between upwelled and oceanic waters produce a complex pattern of regional variability. On the basis of historical data and a series of interdisciplinary field studies, the principal features of the region are described. These include a prominent upwelling filament originating near 28°N off the African coast, cyclonic and anti-cyclonic eddies downstream of the archipelago, and warm wake regions protected from the Trade winds by the high volcanic peaks of the islands. The filament is shown to be a recurrent feature, apparently arising from the interaction of a topographically trapped cyclonic eddy with the outer edge of the coastal upwelling zone. Its role in the transport and exchange of biogenic material, including fish larvae, is considered. Strong cyclonic eddies, observed throughout the year, drift slowly southwestward from Gran Canaria. One sampled in late summer was characterised by large vertical isopycnal displacements, apparent surface divergence and strong upwelling, producing a fourfold increase in chlorophyll concentrations over background values. Such intense eddies can be responsible for a major contribution to the vertical flux of nitrogen. The lee region of Gran Canaria is shown to be a location of strong pycnocline deformation resulting from Ekman pumping on the wind shear boundaries, which may contribute to the eddy formation process.