A layered numerical model for simulating the generation and propagation of internal tides over continental slope II stability analysis

INTRODUCTIONAsoneofthemethodsenablingnumericalsolutionofdifferentialequations,thefinite differ encemethodiswidelyacceptedinthestudyofphysicaloceanography.Afinite differenceschememusthavepropertiesofconvergence ,consistencyandstabilitytoyieldusefulapproximatesolutionoftherelevantdifferentialequations.However,thepropertiesneednotbeverifiedonebyonebecausethewell knownLaxLawassuresthattheconvergenceisequivalenttothestabilityforafinitediffer enceschemewithconsistence .Twomainmethodsforstudyin…     

A layered numerical model for simulating the generation and propagation of internal tides over continental slope III. Numerical experiments and simulation

The layered model in Part I was used to simulate the internal tide in a stratified, two layer, and rectangular sea area with step-like topography. The internal tide current velocities of the upper and lower layers and the interfacial elevations were computed and the effect of the upper layer water depth and density difference were studied. Numerical experiments verified that the model can correctly simulate internal tides. The model was also applied to the northwestern part of the South China Sea to simulate the internal tides there with real topography. The distributions of internal tide amplitude in interfaces were delineated. Contribution No. 3590 from the Institute of Oceanology, Chinese Academy of Sciences. Project 49676275 supported by NSFC and also supported by National Special Research Program 97-926-05-02.     

A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGATION OF INTERNAL TIDES OVER CONTINENTAL SLOPE I. MODEL DESIGN

A layered three-dimensional nonlinear numerical model was constructed to simulate the generation and propagation of internal tides over the continental slope. The simulation was split into external mode computation (EMC) and internal mode computation (IMC) to minimize the computational load. IMC was carried out once after EMC was implemented N times. As to EMC, a semi-implicit numerical scheme was applied in such a way that the pressure gradient terms and the velocity divergence terms were discretized semi-implicitly, but the other terms were discretized explicitly. Eulerian-Lagrangian explicit discretization was applied to the convective terms simultaneously. As a result, the stability of EMC did not depend on the wave celerity and time step was not limited by the CFL condition. More than that, use of the conjugate gradient accelerated Jacobi method further improved the computational efficiency of the model.     

A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGAYION OF INTERNAL TIDES OVER CONTINENTAL SLOPE Ⅰ.MODEL DESIGN

mODUCnONSinceRattw(lwn)develoPedthefirstthcoreticalm0dl0ninternaltides,Inandifferentmodlshavebeenpresented.Theearlym0dlssuchastheonescreatedbyCoxandSandstorm(l962),Baines(l973,l982),etal.wereInainlylinear.Itwasnottmtilthe1980'sthatmodelsforstUdvingthenonlinearclertersofintemaltidesbegant0bedeveloPed.ThempicaloneswerethoseProposedorusedbyPinpeeetal.(1984),Maze(l987),WllmottandEdnds(l987),~(l994),andGerkema(l996).klthoughthesemodlscontribuegnailytoourundrstandingofthegenerationandproPag…     

A TWO-DIMENSIONAL VORTICITY MODEL OF INTERNAL TIDES GENERATED ON THE CONTINENTAL SHELF/SLOPE

A two-dimensional spectral-difference mode (with vorticity and density equations) of internal tides isdeveloped for studying the genration and propagration of internal tides generated at the continentalshelf/slope. In general, internal tides propagate seaward in deep sea regions and shoreward on the shelf,and are dissipated rapidly. When the Vaisala frequency decreases vertically, waves may be mostly limited to thecontinental slope region. in deep sea region, motions may have either boam-like structure or modal structure,depending on the stratification strerigth and structure, whereas a modal structure may always exist onthe shelf. Waves show strong bottom intensification on the slope when strong stratification exists on thebottom. The barotropic tidal advection may affed the temporal character of internal tides at thecontinental slope, shelf break and shelf regions. but may have little influence on the energy density and energy flux of internal tides. ln the case of strong stratification, waverforms of     

Theoretical study of the effect of topographic height and width on generation of internal tides

Internal tides generated upon two-dimensional Gaussian topographies of different sizes and steepness are investigated theoretically in a numerical methodology. Compared with previous theoretical works, this model is not restricted by weak topography, but provides an opportunity to examine the influence of topography. Ten typical cases are studied using different values of height and/or width of topography. By analyzing the baroclinic velocity fields, as well as their first eight baroclinic modes, it is found that the magnitude of baroclinic velocity increases and the vertical structure becomes increasingly complex as height increases or width decreases. However, when both height and width vary, while parameter s （the ratio of the topographic slope to the characteristic slope of the internal wave ray） remains invariant, the final pattern is influenced primarily by width. The conversion rate is studied and the results indicate that width determines where the conversion rate reaches a peak, and where it is positive or negative, whereas height affects only the magnitude. High and narrow topography is considerably more beneficial to converting energy from barotropic to baroclinic fields than low and wide topography. Furthermore, parameter s, which is an important non-dimensional parameter for internal tide generation, is not the sole parameter by which the baroclinic velocity fields and conversion rate are determined.     

AN EXACT SOLUTION OF INTERNAL TIDES GENERATED AT CONTINENTAL SLOPE

By using a coordinate transformation,an exact solution of internal tides is obtained when the bot- tom slope is linear and the V(?)is(?)la frequency is constant.Consequently the dispersion relations of free waves are presented.Compared with Baines solution,the solution derived here is more consistent with experiment     

PROGRESS OF STUDIES ON THE INTERNAL TIDE GENERATED BY THE PASSAGE OF BAROTROPIC TIDE OVER CONTINENTAL SHELF/SLOPE

Various aspects of studies on internal tides are reviewed .Both beam-like structure and modal structure of internal tides may exist in the ocean . Bottom intensifications are caused by many factors .e.g. upstream blocking , which is the result of nonlinear interaction among waves . The energy may decay very fast so that internal tides are mostly locally generated .Internal tides may have considerable residual currents.In a 3-D frame, numerical study revealed that internal waves may interfere with each other to cause strong motions fer from the generation sources.The mechanism that determines how the lee waves break to form various nonlinear waves such as solitary waves, hydraulic jumps and internal surges or bores remains unclear. Analytic study is difficult , so numerical method may be effective . A radiation condition on the open boundary must be employed. A complete 3-D model may gain interesting result.Study on internal tides in China is limited to field observations and data analysis .     

Energetics and temporal variability of internal tides in Luzon Strait: a nonhydrostatic numerical simulation

A fully nonlinear,three-dimensional nonhydrostatic model driven by four principal tidal constituents(M2,S2,K1,and O1) is used to investigate the spatial-temporal characteristics and energetics of internal tides in Luzon Strait(LS).The model results show that,during spring(neap) tides,about 64(47) GW(1 GW=109 W) of barotropic tidal energy is consumed in LS,of which 59.0%(50.5%) is converted to baroclinic tides.About 22(11) GW of the derived baroclinic energy flux subsequently passes from LS,among which 50.9%(54.3%) flows westward into the South China Sea(SCS) and 45.0%(39.7%) eastward into the Pacific Ocean,and the remaining 16(13) GW is lost locally owing to dissipation and convection.It is revealed that generation areas of internal tides vary with the spring and neap tide,indicating different source areas for internal solitary waves in the northern SCS.The region around the Batan Islands is the most important generation region of internal tides during both spring and neap tides.In addition,the baroclinic tidal energy has pronounced seasonal variability.Both the total energy transferred from barotropic tides to baroclinic tides and the baroclinic energy flux flowing out of LS are the highest in summer and lowest in winter.     

Modification on Lynett and Liu＇s model for internal solitary wave propagation over variable bathymetry

A two-dimensional, depth-integrated model proposed by Lynett and Liu （2002） was checked carefully, and several misprints in the model were corrected after detailed examination on both the theory and the numerical program. Several comparisons were made on wave profile, system energy and maximum wave amplitude. It is noted that the modified model can simulate the propagation of the internal solitary waves over variable bathymetry more reasonably to a certain degree, and the wave profiles obtained based on the modified model can better fit the experiment data reported by Helfrich （1992） than those from original model.     

Propagation of internal waves up continental slope and shelf

In a two-dimensional and linear framework, a transformation was developed to derive eigensolutions of internal waves over a subcritical hyperbolic slope and to approximate the continental slope and shelf. The transformation converts a hyperbolic slope in physical space into a flat bottom in transform space while the governing equations of internal waves remain hyperbolic. The eigensolutions are further used to study the evolution of linear internal waves as it propagates to subcritical continental slope and shelf. The stream function, velocity, and vertical shear of velocity induced by internal wave at the hyperbolic slope are analytically expressed by superposition of the obtained eigensolutions. The velocity and velocity shear increase as the internal wave propagates to a hyperbolic slope. They become very large especially when the slope of internal wave rays approaches the topographic slope, which is consistent with the previous studies.     

A VOF-based numerical model for breaking waves in surf zone

This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes (RANS) equations for a mean flow, and (he k-s equations for turbulence kinetic energy k and turbulence dissipation rate e. To track a free surface, the volume of fluid (VOF) function, satisfying the advection equation was introduced. In the numerical treatment, third-order upwind difference scheme was applied to the convection terms of the RANS equations in order to reduce the effect of numerical viscosity. The shoaling and breaking processes of a periodic wave train on gently sloping beaches were modeled. The computed wave heights of a sloping beach and the distribution of breaking wave pressure on a vertical wall were compared with laboratory data.     

A THREE-DIMENSIONAL THERMOCLINE MODEL FOR THE YELLOW SEA AND NORTHERN EAST CHINA SEA

A time-dependent, three-dimensional finite difference model is presented for simulating the stratifiedYellow Sea and northem East China Sea. The mode is forced by time-dependent observed wind, surfaceflux of heat, and tidal turbulence. With this model, momentum and temperature distribution can be computed,and an approximation for the sub-grid scale effects is introduced by the use of mass and momentumexchange coefficients. The vertical exchanges are quite dependent on these assumed coefficents, whichare complicated functions of the turbulence energy of tide and wind, of the stratified strength and otherfactors. This model was applied to describe the mechanics of the variations in strength and thickness ofthe thermocline covering almost the whole Yellow Sea and northern East Chna Sea in summer. Comparisonsof the computed output with obtained survey data led to some important conclusions.     

A NUMERICAL STUDY OF THE TIDE-SURGE INTERACTION IN THE EAST CHINA SEA AND THE SOUTH CHINA SEA

Nearshore sea levels in the East China Sea(ECS) and the South China Sea(SCS) during tropical cyclones-Typhoon 8007(Joe, 1980) and Typhoon 7209(Betty 1972) were simulated. The tide-surge interactions in the two regions are remarkable and locally produced. The corresponding nonlinear effects were derived from the different nonlinear terms. The contribution of the quadratic friction term is the most important, the shallow term comes second the convective term is the least; the phases of the interactions generated by the various nonlinear terms are asynchronous. Both the quadratic friction and the convective term can stimulate and aggravate the surge structure with more peaks. The bottom friction features have crucial influences on tides and surges, and the interaction is sensitive to the changes of tide and surge.     

A THREE-LAYER OCEAN CIRCULATION MODEL APPLICATION TO NUMERICAL STUDIES ON THE NORTH PACIFIC OCEAN CIRCULATION

The formulation and justification of a three-layer baroclinic ocean model developed to simulate thegeneral circulation of the ocean are described in this paper.Test of the model in simulating the annualmean circulation patterns in the North Pacific under the prescribed atmospheric forcing,which consists ofthe climatological surface wind stress and sea surface heat flux,and comparison of the results withobservations showed that the model basically simulated the large scale features of the annual meancirculation patterns in the North Pacific Ocean such as those of the intensified western boundary currentsand the North Equatorial Currents and Undercurrents.But due to the coarse resolution of the model,some details of these currents were poorly reproduced.The seasonal variations of the North Pacific Oceancirculation driven by the seasonal mean sea surface wind stress was calculated,the different aspects of theseresults were analyzed and the main current(the intensified western boundary currents)transports we     

民航京沪穗数值预报系统在广州的本地化试验

为了调整优化基于WRF模式的民航京沪穗数值预报系统在广州本地的预报效果,使用3组不同的物理参数化方案和资料同化方案组合,对发生在2011年10月13日~14日广东地区的暴雨过程进行模拟。降水预报结果显示不同物理参数化方案和资料同化方案对降水预报有较大的影响,使用香港城市大学大气研究实验室实时预报系统推荐的参数化方案的降水预报好于加拿大温哥华地区业务运行的参数化方案,使用香港的方案,不同化自动站资料的预报效果好于同化自动站资料。而环流形势场、相对湿度场、水汽通量场和CAPE指数场对不同参数化方案的敏感性要小于降水场,另外还分析了系统连续15天预报结果。最终结果表明,不论是降水场还是形势场,使用香港城市大学的方案并且不同化自动站资料的评分优于其他2种方案,可以作为广州本地业务方案使用。     

ADI barotropic ocean model for simulation of Kuroshio intrusion into China southeastern waters

In this numerical model for simulating the Kuroshio intrusion into the East and South China Seas, vertically averaged marine hydrodynamic equations governing ocean currents and long-period waves are approximated by a set of two-time-level semi-implicit fimite difference equations. The major terms including the local acoeleration, sea-surface slope, Coriolis force and the bottom friction are approximated with the Crank-Nicholson scheme, which is of second order accuracy. The advection terms are approximated with the Leith scheme. The difference equations are split into two sets of alternating direction implicit equations, each of which has a tridiagonal matrix and can be easily solved. The model reproduces a major Kuroshio intrusion north of Luzon Island, one north of Taiwan Island, and one west of the Tokara Strait. The model shows a current system running from the Luzon Strait to the coast of Vietnam and Hainan Island, through the Taiwan Strait and then into the Tsushima Strait. The summer and winter monsoons generate several eddies in the South China Sea. Project supported by the National Natural Science Foundation of China.     

NUMERICAL STUDY OF THE INFLUENCE OF WAVES AND TIDE-SURGE INTERACTION ON TIDE-SURGES IN THE BOHAI SEA

Abstract The author‘s combined numerical model consisting of a third generation shallow water wave model and a 3-D tide-surge model with wave-dependent surface wind stress were used to study the influence of waves on fide-surge motion. For the typical weather case, in this study, the magnitude and mechanism of the influence of waves on tide-surges in the Bohai Sea were revealed for the first time. The results showed that although consideration of the wave-dependent surface wind stresses raise slightly the traditional surface wind stress, due to the accumulated effects, the computed results are improved on the whole. Storm level maximum modulation can reach 0.4 m. The results computed by the combined model agreed well with the measured data.     

沿海和岛屿重力海潮负荷改正模型——以马祖岛为例

基于NAO99b全球海潮模型、NAO99Jb区域海潮模型、验潮站资料和SRTM地形数据确定的高空间分辨率海陆边界数据,构建我国沿海和岛屿高精度重力海潮负荷改正模型。以马祖岛为例介绍该模型,并采用实测的绝对重力测量资料进行验证。结果表明,经该模型改正后的重力观测精度明显提高。