The baroclinic residual circulation in shallow seas

There are two different modeling approaches which have been proposed and utilized to derive residual currents: the first approach is equivalent to deducing residual currents from current-meter records using filtering techniques or time averages of time-series records to remove tidal variations; in the second approach, filters or time averages over several tidal cycles are applied to the hydrodynamic equations to generate the governing equations for residual circulation. Based on the latter, both the baroclinic dynamic models of residual circulation are proposed, of which one is a two-dimensional transport model and the other is a three-dimensional model with variable eddy viscosity. The two-dimensional transport model is a direct generalization from the barotropic model of residual circulation presented by Nihoul and Randy (1975) and Heaps (1978) to the baroclinic model. In the three-dimensional model with variable eddy viscosity, using a Sturm-Liouville system adopted in the reference [5], the nondimensional problem for residual circulation reduces to the nondimensional problem of the elevation and the expression of residual currents. It should be pointed out that both the baroclinic models developed in the present paper are confined to describe the Eulerian residual circulation only.     

Directional spectrum analysis of internal waves in the sea off Sydney,Australia

The directional-spectrum model of internal waves in shallow seas given by Xiao and Fang (1991) was used to analyze the observation data gathered in April, 1981, in the sea off Sydney, Australia. Some reasonable results were obtained. The energy ratio between Wavemodes 1 and 2 was about 2 for most frequencies and was up to 8 at ω=0.23 cph. Wave components with frequencies 0.1–0.8 cph were generated in the deep sea, and propagated onshore, while those with frequencies higher than 0.8 cph were locally generated by the interaction between longshore currents and bottom topography. Several surveys were carried out in the sea off Sydney, Australia (Cresswell, 1974, Cresswell and Boland, 1981, and Fang, Boland and Cresswell, 1984). The survey performed in April 1981 by Fang, Boland and Cresswell (1984) was outstandingly successful. To draw some deterministic and stochastic characters of internal waves, Fang, Boland and Cresswell (1984) and Fang (1987) analyzed these data gathered in 1981 and obtained some reasonable results.     

Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas

Some approximate formulas, based on the internal- wave directional spectral model established by Schott and Willebrand (1973), of vertically standing wavemode eigenfunctions and a dispersion relation of internal waves in shallow seas are presented. An optimization method to estimate internal wave directional spectra is described and the confidence interval expression of the estimates is established. The GM spectral model of oceanic internal waves cannot be used in shallow seas (01 bers, 1983). Internal waves in shallow seas have two origins: oceanic (those generated in and propagating from the deep sea and ocean) and local (Phillips, 1977). As both reveal obvious propagation orientations, it is important to investigate the directional properties of the internal wave field. Though cross correlation function or cross-spectrum analyses can reveal the directional properties in some degree (Fang et al., 1984, and Fang, 1987), internal- wave directional spectrum analysis can further estimate the main propagation directions of wave components with different modenumbers and frequencies. So the latter is a more effective analysis tool. Because internal- wave directional spectrum analysis requires high quality data and long computer time, there are very few study reports so far on this subject. Among them. Schott and Willebrands' (1973) work is noteworthy. On the supposition, of linearization, they derived an internal- wave directional spectrum model. Internal-wave directional-spectra in shallow seas are investigated in the present study with their work as reference. Project supported by the National Natural Science Foundation of China.     

On the Lagrangian residual current and residual transport in a multiple time scale system of shallow seas

A multiple time scale perturbation method is used to discuss the Lagrangian residual current and residual transport on the basis of a weakly nonlinear dynamic model of shallow seas. The governing equations for the long-term variation of zero order “apparent concentration” (which is a linear combination of salinity, temperature of seawater and the concentration of any tracer which is conservative and passive) and its mean value over tidal cycles are obtained for the system with single tidal constituent, and for the one with multi-constituents, winds and thermohaline. The equations for the two cases are in the same form and show this long-term variation resulted from the cumulative effect of residual convection and turbulent diffusion. The multiple time scale variation of current is caused by tides, winds, and the thermohaline and the nonlinear effects of the system. The derived set of governing field equations of the Lagrangian current for this multiple time scale system is also in the same form as that for a single time scale system.     

Underwater topography detection of Taiwan Shoal with SAR images

Under suitable conditions of tidal current and wind, underwater topography can be detected by synthetic aperture radar (SAR) indirectly. Underwater topography SAR imaging includes three physical processes: radar ocean surface backscattering, the modulation of sea surface short wave spectrum by the variations in sea surface currents, and the modulation of sea surface currents by the underwater topography. The first process is described usually by Bragg scattering theory because the incident angle of SAR is always between 20°–70°. The second process is described by the action balance equation. The third process is described by an ocean hydrodynamic model. Based on the SAR imaging mechanism for underwater topography, an underwater topography SAR detection model and a simplified method for its calculation are introduced. In the detection model, a two-dimensional hydrodynamic model — the shallow water model is used to describe the motion of tidal current. Due to the difficulty of determining the expression of SAR backscattering cross section in which some terms can not be determined, the backscattering cross section of SAR image used in the underwater topography SAR detection is pro-processed by the simulated SAR image of the coarse-grid water depth to simplify the calculation. Taiwan Shoal, located at the southwest outlet of Taiwan Strait, is selected as an evaluation area for this technique due to the occurrence of hundreds of sand waves. The underwater topography of Taiwan Shoal was detected by two scenes of ERS-2 SAR images which were acquired on 9 January 2000 and 6 June 2004. The detection results are compared with in situ measured water depths for three profiles. The average absolute and relative errors of the best detection result are 2.23 m and 7.5 %, respectively. These show that the detection model and the simplified method introduced in the paper is feasible.     

THE DEPENDENCE OF WIND STRESS ON SEA STATE

Based on up to date literature, this paper details the evolution of wave dependence of wind stress.Some typical models of the dependence of wind stress on waves are described in detail. Although there isno universally accepted theory and model, recent studies indicate that the wind strees strongly dependson the development state of sea waves, i. e., young seas are rougher than mature seas, in other words, thewind stress decreases with increasing wave age.     

Effects of wind input and wave dissipation formulations on the steady Ekman current solution

The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered： one from the wave modeling （WAM） program proposed by Hasselmann and Komen and the other provided by Tsagareli and Babanin. The solution adopted for our study was presented by Song for the wave-modified Ekman current model that included the Stokes drift, wind input, and wave dissipation with eddy viscosity increasing linearly with depth. Using the Combi spectrum with tail effects, the solutions are calculated using two formulations for wind input and wave dissipation, and compared. Differences in the results are not negligible. Furthermore, the solution presented by Song and Xu for the eddy viscosity formulated using the K-Profile Parameterization scheme under wind input and wave dissipation given by Tsagareli and Babanin is compared with that obtained for a depth-dependent eddy viscosity. The solutions are further compared with the available well-known observational data. The result indicates that the Tsagareli and Babanin scheme is more suitable for use in the model when capillary waves are included, and the solution calculated using the K-Profile Parameterization scheme agrees best with observations.     

Wind energy input in coastal seas east of China

This study investigates the wind energy input, an important source of mechanical energy, in the coastal seas east of China. Using the wind field from the high-resolution sea surface meteorology dataset in the Bohai Sea, Yellow Sea, and East China Sea, we studied the wind energy input through surface ageostrophic currents and surface waves. Using a simple analytical formula for the Ekman Spiral with timedependent wind, the wind energy input through ageostrophic currents was estimated at ～22 GW averaged from 1960 to 2007, and through use of an empirical formula, the wind energy input through surface waves was estimated at ～169 GW. We also examined the seasonal variation and long-term tendency of mechanical energy from wind stress, and found that the wind energy input to the East China Sea decreased before the 1980s, and then subsequently increased, which is contrary to what has been found for the Bohai Sea and Yellow Sea. More complicated physical processes and varying diffusivity need to be taken into account in future studies.     

Numerical study on inter-tidal transports in coastal seas

Inter-tidal(subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al.(2008), an updated Lagrangian inter-tidal transport equation, as well as new concept of Lagrangian in- ter-tidal concentration(LIC), has been proposed for a general nonlinear shallow water system. In the present study, the LIC is nu- merically applied for the first time to passive tracers in idealized settings and salinity in the Bohai Sea, China. Circulation and tracer motion in the three idealized model seas with different topography or coastline, termed as ‘flat-bottom', ‘stairs' and ‘cape' case, re- spectively, are simulated. The dependence of the LIC on initial tidal phase suggests that the nonlinearities in the stairs and cape cases are stronger than that in the flat-bottom case. Therefore, the ‘flat-bottom' case still meets the convectively weakly nonlinear condi- tion. For the Bohai Sea, the simulation results show that most parts of it still meet the weakly nonlinear condition. However, the de- pendence of the LIS(Lagrangian inter-tidal salinity) on initial tidal phase is significant around the southern headland of the Liaodong Peninsula and near the mouth of the Yellow River. The nonlinearity in the former region is mainly related to the complicated coast- lines, and that in the latter region is due to the presence of the estuarine salinity front.     

Numerical analysis of the nonlinear parameterization of waves in currents over a submerged sill with a non-hydrostatic model

An investigation of the effects of a uniform current strength direction (following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH, a non-hydrostatic numerical wave model. The nonlinear parameters (i.e., asymmetry, skewness, and kurtosis) are calculated, and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured. In the shoaling area of the submerged sill, the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction. Whereas nonlinear parameters grow with the strengthening of the following currents over the crest, they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.     

THE DYNAMIC EFFECTS OF A FINITE DEPTH AMBIENT FLUID ON BOTTOM EDDY

Scaling analysis shows that if o(ε~2, β_1ε, γε) ~o (δ), frontal geostrophic dynamics governs the behav-ior of an isolated bottom eddy in a finite depth ambient fluid; and that the ambient flow induced bybottom eddy migration satisfies quasi-geostrophic dynamics. This two layer model includes the impor-tant processes of advection of bottom eddy due to ambient flow, baroclinic instability, and form dragintroduced by Rossby waves. The numerical results show that the three processes enhance theinstability and alter the migration speed of the bottom eddy, and that the form drag induces asignificant meridional drift of the eddy.     

Numerical Simulation of Wintertime Mesoscale Eddies in the East China Sea

INTRODUCTIONAnimportantachievementofoceanographysincethe 1960swasthediscoveryofmesoscaleed dieswithspatialscaleofhundredsofmeters,andtimescaleofhours;andaverageflowvelocityofabout 10cm s.Theenormousenergyofthemesoscaleeddyiscomparabletothatofacycloneoran ticycloneintheatmosphere .Themesoscaleeddyisoneoftheimportantfactorsthatdecidethechangeoftheocean .Intherecentdecades,ChineseandforeignscientistshavedonelotsofworkontheEastChinaSeasmesoscaleeddies,theformationmechanismofwhicharethefocuso…     

Equation on spatial variation of shallow water waves amplitude

Boussinesq’s theory was used in this study on water waves entering shallow water showing that the spacial variation of the wave amplitude is nonlinear, and is governed by the Duffing equation usually applied to describe nonlinear oscillation in nature. Contribution No. 3324 from the Institute of Oceanology, Chinese Academy of Sciences. Project 49471276 supported by NSFC and the Ninth-Five-Year Key Project (KI952-s1-420) of the Chinese Academy of Sciences.     

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV （Korteweg-de Vries） equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.     

IGGGRACE01S模型确定的海面地形和地转流

用IGGGRACE01S、EIGENGRACE02S和EGM96地球重力场模型的前80阶分别计算出全球大地水准面,再与多颗测高卫星资料得到的平均海面高模型KMS04差分,构制出3种海面地形,并计算出相应的地转流。与Williams绘制的全球主要海流结果相比,不难看出,重力场模型IGGGRACE01S、EIGENGRACE02S的结果能清晰地显示出大尺度海洋地转流,而EGM96模型结果在赤道地带不明显。上述结果不仅显示了GRACE地球重力场模型IGGGRACE01S和EIGENGRACE02S具有较高精度探测地转流的能力,而且也表明了它们的长波精度优于EGM96模型,从应用角度展示了GRACE结果的有效性。     

Numerical simulation of scatterometer assimilated wind and ocean wave in eastern China seas and adjacent waters

Using the latest version of Mesoscale Modeling System (MM5v3), we assimilated wind data from the scatterometer and built a model to assimilate the wind field over eastern China seas and adjacent waters and applied the wave model WAVEWATCH-Ⅲ to test the sea area with assimilative wind and blended wind of QSCAT and NCEP as driving forces. High precision and resolution numerical wave results were obtained. Analysis indicated that if we replace the model wind result with the blended wind, better sea surface wind results and wave results could be obtained.     

Coastal upwelling and coastal jets in continuously stratified seas

Nonlinear numerical models of continuously stratified seas are developed for vertical sections to study the mechanism of coastal upwelling and coastal jets in two kinds of seas: the so-called finite or closed sea bounded by two vertical coastal coasts, without elevation of sea surface, but with a flat bottom; and the semi-infinite sea bounded by only one vertical coast, with both an elevation of sea surface and a flat or inclined bottom. Constant wind stress in the first case, and constant wind stress or negative wind stress curl in the second case, are abruptly imposed. The key procedure for the mathematical analysis is to calculate the horizontal pressure gradient first by a special treatment. In the first case, the variation of horizontal components of velocity is changed with time to show three successive time intervals. The results show that the width of baroclinic jets depends upon (σS)^1/2, and that distribution of isopycnic lines delineates the warm and cold regions. The relative importance of each term in the equilibrium among forces is thus determined. Distribution of stream function in vertical section reveals the upper and bottom Ekman layers. Two coastal jets are found with different alongshore velocities. The distribution of density anomalies displays the horizontal diffusion adjustment. An unstable case appears at different surface boundary conditions. In the second case, the vertical velocity will be stronger in the sea with less stratification, with an inclined bottom, and with a negative wind stress curl. The horizonatal offshore velocity increases in strength in a sea with inclined bottom and with negative wind stress curl. The vertical circulation pattern reveals the upwelling only. The distribution of density shows the isopycnic lines lifted upward near the shores. Obviously, the range of elevation of sea surface near the shore is larger than that far offshore. The jet width is less than the Rossby radius of deformation. A stronger jet will occur in more shallow water with negative wind stress curl. The coastal jet does not develop when the coefficient of horizontal turbulence increases to a certain limiting value.     

Wave Pressure Acting on V-Shaped Floating Breakwater in Random Seas

Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.     

A THIRD GENERATION SHALLOW WATER WAVE NUMERICAL MODEL-YE-WAM

This paper pnesents a third gneration shallow Whter disode spedtal wave nbotal medeIYE-WAM based on the spedtal action balance equation. The mode accounts for all edevan effectsof currents on waves, incuding tmpotally and spatialy varying depth and current inded refraction,sttalning and fequency shift and also explidtly takeS into aanunt all source terms, speclally adePth-limited breaking dheipation. In addition, an energy forcing scheme is propond and applied to themode's open boundaries to areUn for the propagution of sedIs into the study spstem The upwinddiffeIenng scheme and a standard hybrid diffdrencing scheme for the propagaion terrn and a simpleEuler method for the source teme are employed.