A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGATION OF INTERNAL TIDES OVER CONTINENTAL SLOPE Ⅲ. NUMERICAL EXPERIMENTS AND SIMULATION

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Internal Tide Generation and Dissipation by Small Periodic Topography in Deep Ocean

Internal tides generated by a rough sea floor are an important source of mixing in the abyssal ocean. Two linear models are employed to evaluate the conversion rate from barotropic tides to internal tides and the energy distribution in each mode. Considering the periodicity of internal tides, the topography is represented by periodically distributed knife edges and sinusoidal ridges within one wavelength of mode-1 internal tides. The knife edges generate greater internal tides than the sinusoidal ridges due to their sharp shape, which approximates an extremely supercritical condition. Energy flux concentrates in modes whose numbers are multiples of the knife edge or ridge number. Then, a fully nonlinear model that integrates viscosity and diffusion is implemented, and its results are compared with those of the linear model. Internal wave rays generated in the nonlinear model show a distribution similar to the linear models' prediction. High dissipation rates coincide with the rays, suggesting that nonlinear wave-wave interaction is a dominant mechanism for internal tide dissipation in the abyssal ocean.     

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

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. Contribution No. 3588 from the Institute of Oceanology, Chinese Academy of Sciences. Project 49676275 supported by NSFC and National Special Research Program 97-925-05-02.     

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 investigation of the properties of low-frequency internal waves in the northeastern China Seas

A simple and practical method for separating low-frequency internal waves from low-frequency barotropic waves was employed to analyze the observation data. Analysis of some data gathered in the northestern China Seas revealed strong semidiurnal internal tides and near-inertial internal waves at the stations in the East China Sea and near-inertial waves but no semidiurnal internal tides at the station in the centre of the Yellow Sea. The geographic properties of low-frequency internal waves in the region are discussed primarily on the basis of the mechanism of internal tide generation on the continental shelfbreak, and the mechanisms of local generation and global generation. Project supported by the National Natural Science Foundation of China.     

Observation of Internal Tides in the Qiongzhou Strait by Coastal Acoustic Tomography

In this study, power spectral density and inverse analyses were performed to obtain the frequency characteristics and spatial distribution of temperature in the Qiongzhou Strait using reciprocal sound transmission data obtained in a coastal acoustic tomography experiment conducted in 2013. The results reveal three dominant types of internal tides(diurnal, semidiurnal, and terdiurnal).Spectral analysis of the range-average temperature deviation along the northern and southern transmission paths shows that along the northern path, the energy of the diurnal internal tides was significantly larger than that of the semidiurnal tides. The semidiurnal internal tides, in contrast, were more pronounced along the southern path. A terdiurnal spectrum with an energy level equivalent to that of the semidiurnal internal tide was discernable for both the northern and southern paths. These three types of internal tides can also be recognized in the time variation of the zonal-average temperature deviation. The diurnal internal tides were strengthened along the northern coast, implying their westward propagation and the existence of coastally trapped effects. The other two types of internal tides, which have smaller wavelengths than the diurnal internal tides, were less resolved over the entire tomographic domain due to the insufficient resolution of the inversion. The data quality was verified to be satisfactory by error estimation.     

Seasonal evolution of circulation and thermal structure in the Yellow Sea

In this paper, the authors used the Princeton Ocean Model (POM) to simulate the seasonal evolutions of circulation and thermal structure in the Yellow Sea. The simulated circulation showed that the Yellow Sea Warm Current (YSWC) was a compensation current of monsoon-driven current, and that in winter, the YSWC became stronger with depth, and could flow across the Bohai Strait in the north. Sensitivity and controlling tests led to the following conclusions, In winter, the direction of the Yellow Sea Coastal Current in the surface layer was controlled partly by tide instead of wind, In summer, a cyclonic horizontal gyre existed in the middle and eastern parts of the Yellow Sea below 10 m. The downwelling in upper layer and upwelling in lower layer were somehow similar to Hu et al. (1991) conceptual model. The calculated thermal structure showed an obvious northward extending YSWC tongue in winter, its position and coverage of the Yellow Sea Cold Water Mass in summer.     

Nonlinear interaction between astronomical tides and storm surges at wusong tidal station

There are obvious periodic oscillations in the observations of storm surges in the East China Sea. The storm surges are not only controlled by the wind stresses and isolated long wave caused by typhoons but also affected by the interaction between astronomical tides and storm surges. In the present paper we simulate the interaction between tides and storm surges by using a two dimensional numerical model. In our numerical experiments we use the data of the storm surge induced by Typhoon 8114. The calculations tally with the measured data well. The results indicate that the periodic oscillations occurring in the elevations of the surge are mainly caused by the interaction between the tide and the storm surge. The numerical experiments also indicate that the forecasting precision may be notably improved if the nonlinear interaction between tides and storm surges is taken into account.     

Global ocean tides from Geosat altimetry by Quasi-Harmonic analysis

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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.     

Estimation of the Reflection of Internal Tides on a Slope

Reflection occurs when internal tides impact on a steep continental slope. Separating reflected internal tide signals from incident ones is crucial to develop the parameterization of internal tide-driven turbulent mixing on the continental slopes. In this study, the performances of three different methods for estimating internal tide reflections are examined by using two different cases. The Hilbert transform-based method is found to be more suitable than two other methods for both cases considered in this study. The two other methods are effective for westward-propagating mode-1 internal tides impacting a slope, but inappropriate in the case where internal tides radiate from a Gaussian ridge impact the slope because of their inaccurate estimation of incident internal tides in the latter case. Such inaccurate estimation further influences the extraction of reflected signals and calculation of the reflected and cross term of energy fluxes. In addition, it should be noted that, due to the use of filtering, the method based on Hilbert transform may result in slight bias when assessing the incident and reflected signals near topographic features.     

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow. One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained. The model simulations describe the generation and propagation of internal waves well. When the strength of imposed barotropic tides and the water stratification stay unchanged, the steepness of the sill slope can control both (a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves, and (b) the amplitude of the internal solitary waves generated. If the steepness of the sill is asymmetric, the nonlinear internal solitary waves may be induced on the steeper side of the sill. These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.     

Impact of estuarine reclamation projects on saltwater intrusion and freshwater resource

Estuarine projects can change local topography and influence water transport and saltwater intrusion. The Changjiang (Yangtze) River estuary is a multichannel estuary, and four major reclamation projects have been implemented in the Changjiang River estuary in recent years: the Xincun Shoal reclamation project (RP-XCS), the Qingcao Shoal reclamation project (RP-QCS), the Eastern Hengsha Shoal reclamation project (RP-EHS), and the Nanhui Shoal reclamation project (RP-NHS). The effects of the four reclamation projects and each project on the saltwater intrusion and water resources in the Changjiang River estuary were simulated in a 3D numerical model. Results show that for a multichannel estuary, local reclamation projects change the local topography and water diversion ratio (WDR) between channels and influence water and salt transport and freshwater utilization in the estuary. During spring tide, under the cumulative effect of the four reclamation projects, the salinity decreases by approximately 0.5 in the upper reaches of the North Branch and increases by 0.5–1.0 in the middle and lower reaches of the North Branch. In the North Channel, the salinity decreases by approximately 0.5. In the North Passage, the salinity increases by 0.5–1.0. In the South Passage, the salinity increases by approximately 0.5 in the upper reaches and decreases by 0.2–0.5 on the north side of the middle and lower reaches. During neap tide, the cumulative effects of the four reclamation projects and the individual projects are similar to those during spring tide, but there are some differences. The effects of an individual reclamation project on WDR and saltwater intrusion during spring and neap tides are simulated and analyzed in detail. The cumulative effect of the four reclamation projects favors freshwater usage in the Changjiang River estuary.

     

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.     

A numerical study on the generation of a distinct type of nonlinear internal wave packet in the South China Sea

A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Experiment in 2001. Data analysis shows that the occurrence of the distinct internal wave packet is closely related with the occurrence of lower-high internal tides; the internal tides are mixed in the experimental area and, thus, there is diurnal inequality between the heights of two neighboring internal tides. Modeling of internal tides and internal solitary waves in a shoaling situation suggests that this type of wave packet can be generated in the South China Sea by the large shoaling of internal solitary waves and internal tides. Both the internal solitary waves and the internal tides come from the direction of Luzon Strait. The initial large internal solitary waves contribute to the occurrence of the largest internal solitary wave in the middle of the packet and the waves behind the largest internal solitary wave, while the shoaling internal tides bring about the nonlinear internal waves in front of the largest internal solitary wave via interaction with the local shelf topography.     

Seasonal Variability of Internal Tides Northeast of Taiwan

The spatial-temporal characteristics of the barotropic tides and internal tides(ITs) northeast of Taiwan Island are examined, based on a 1-year mooring current observations from May 23, 2017 to May 19, 2018. The results of harmonic tidal analysis show that the barotropic tides are dominated by semidiurnal tides, which is mainly controlled by M_2 tidal components. Moreover, the vertical structures of diurnal and semidiurnal ITs show that the semidiurnal IT shows notable seasonal variation, whereas seasonal variations of the diurnal IT energy is not significant. The semidiurnal IT energy in winter half year is twice that in summer half year. The seasonal variation of semidiurnal IT is mainly modulated by the direction change of the current rather than by the topographic features and stratification. In summer(winter) half year cyclonic(anti-cyclonic) eddies meanly control at this point, so the flow direction is mainly in the southwest(northeast) direction, causing the background flow to flow along(perpendicular to) the isobath. When crossing the isobath, the ITs are generated by the interaction of the barotropic tide and the topography, resulting in the increase of the tidal energy in the winter half year.     

Coupled physical-ecological modelling of the central part of Jiaozhou Bay I. Physical modelling

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

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A numerical study on water diversion ratio of the Changjiang (Yangtze) estuary in dry season

We studied the flood, ebb and tidal averaged along (net) water diversion ratio (WDR) during dry season in the Changjiang (Yangtze) estuary, China, along with the effects of northerly wind, river discharge, tide and their interactions on WDR using the improved version of three-dimensional numerical model ECOM. Using data for annual mean wind speed and river discharge during January, we determined that the flood, ebb, net WDR values in the North Branch of the estuary were 3.48%, 1.68%, −4.06% during spring tide, and 4.82%, 2.34%, −2.79% during neap tide, respectively. Negative net WDR values denote the transport of water from the North Branch into the South Branch. Using the same data, the corresponding ratios were 50.09%, 50.92%, 54.97%, and 52.33%, 50.15%, 43.86% in the North Channel and 38.56%, 44.78%, 103.96%, and 36.92%, 43.17%, 60.97% in the North Passage, respectively. When northerly wind speed increased, landward Ekman transport was enhanced in the North Branch, increasing the flood WDR, while the ebb WDR declined and the net WDR exhibited a significant decrease. Similarly, in the North Channel, the flood WDR is increased, the ebb WDR reduced, and the net WDR showed a marked decrease. In the North Passage, the flood WDR also increased while the ebb and net WDR declined. As the river discharge increased, the flood and ebb WDR of the North Branch increased slightly and the net WDR increased markedly. In the North Channel the flood and ebb WDR changed very slightly, while the net WDR declined during spring tides and increased during neap tides. The WDR in the North Passage changed slightly during flood and ebb tides while the net WDR showed a marked increase. The WDR values of different bifurcations and the responses to northerly wind, river discharge, and tide are discussed in comparison with variations in river topography, horizontal wind-induced circulation, and tidal-induced residual current.     

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