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1.
With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.  相似文献   

2.
The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.  相似文献   

3.
Liu  Guangliang  Liu  Zhe  Gao  Huiwang  Gao  Zengxiang  Feng  Shizuo 《Ocean Dynamics》2012,62(10):1443-1456

The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M 2 tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.

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4.
The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M 2 tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.  相似文献   

5.
In a weakly nonlinear tidal system, the depth-averaged equations for the first-order Lagrangian residual velocity (LRV) are deduced systematically. For the case of a narrow bay, the equations are solved analytically and the results for a specific bottom profile are discussed in detail. According to the pattern of the first-order LRV, the bay can be divided into three parts, namely an inner part, a transitional zone, and an outer part. For the given depth profile, the streamline of the first-order LRV for a shorter bay is a part of that for a longer bay. The first-order LRV depends on a nondimensional parameter that combines the influences of the bottom friction coefficient, the tidal period and the averaged water depth. The form of the bottom friction also has a significant influence on the first-order LRV. The second-order LRV, i.e., the Lagrangian drift, is analytically solved and shows dependence on the initial tidal phase. The LRV differs from the Eulerian residual transport velocity both quantitatively and qualitatively. It is demonstrated that the residual currents obtained according to other definitions may cause misunderstanding of the mass transport in water exchange applications.  相似文献   

6.
Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L b , π/L b ], where L b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.  相似文献   

7.
Abstract

Results are presented of calculations on the generation of residual vorticity by tidal currents over the bottom topography of the Southern Bight of the North Sea. A typical order of magnitude is 10?6 to 10?7 s ?1. This is compared with current measurements on calm days, when similar magnitudes are found. At windspeeds less than about 5 m/s tidal generation of residual vorticity is important; at higher windspeeds wind effects begin to dominate. Our results are relevant in understanding the spatial variability of residual currents, because a non-zero vorticity implies the existence of horizontal gradients in the residual current field.  相似文献   

8.
The 3D first-order Lagrangian residual velocity (LRV) equation is established, and its analytical solution is obtained in a narrow bay. The results show clearly the 3D structure of the first-order LRV. When the exponential bottom profile is assumed, the upper half layer of the water flows in through the deep channel from the open boundary directly to the head of the bay. Then the water will return to the area surrounding the lower half of the inflow area. The downwelling area is located mainly at the deep channel, while the upwelling area occupies both sides of the bay. The inter-tidal water transport, obtained by integrating the 3D first-order LRV through the water column, has a pattern similar to the previous study in which the 2D depth-averaged Lagrangian residual current equations were solved. The inter-tidal water transport is used to analyze the water exchange, and it is found that the water exchange at different cross sections increases smoothly with the distance between the cross sections and the head of the bay until about one wavelength. It is also found that the pattern of the breadth-averaged Lagrangian residual current varies with the length of the bay if a non-flat bottom profile is used. The depth-integrated LRV and the breadth-averaged LRV are mainly determined by the different terms of the tidal body force, with the former determined by the bottom friction related term and the latter by the eddy viscosity related term. When the bay is longer than one wavelength, different results in the outer bay can be observed.  相似文献   

9.
The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.  相似文献   

10.
The dynamics of a single vortex on a beta-plane is discussed in this paper. A barotropic, an equivalent barotropic, one-and-a half and two-layer models are considered. The momentum and energy balances are used to describe the evolution of a vortex. A quasi-stationary balance of the Rossby, Zhukovsky-Kutta forces and the force induced by Rossby-wave radiation, describes the dynamics of the barotropic vortex. A net Coriolis force occurs if the fluid is stratified. The difference between the dynamics of cyclones and anticyclones results directly from the Coriolis force acting on a single vortex in a stratified fluid.All vortices radiate Rossby waves in the quasigeostrophic approximation but intense anticyclones propagate steadily in a one-and-a half layer model. A critical amplitude that bounds radiating and steadily propagating anticyclones is found. Steady propagation of anticyclones in general is impossible in a two-layer fluid due to the radiation of a barotropic Rossby-wave. Some solutions of solitary wave type which are known for a two-layer model, survive owing to wave interference.A single vortex can extract energy from a Rossby wave if synchronism conditions are satisfied. The wave interference again plays a crucial role in this case. The wave interference also determines the energy exchange of vortices located at larger distances. If the distance between the vortices is shorter than the length of the radiated waves, modon may be formed due to a small energy loss.The unbounded monotonic variation of the planetary vorticity is a characteristic feature of a beta-plane approximation. As a result, a single vortex propagates up to a 'rest latitude' where it disappears. The evolution of a single barotropic vortex over bottom topography provides another example of a background vorticity distribution with a local extremum above hills (valleys) or ridges (troughs). Physics of its movement differs from a beta-plane case, but if a vortex lies over broad topography, equations are similar and the evolution of a vortex manifests the same typical features. Particularly, a cyclonic vortex tends to drift to the top of a hill or a ridge. An anticyclonic vortex, on the contrary, slides to the bottom of a valley or a trough.An interaction of a barotropic vortex with a broad mean flow is tractable qualitatively on the basis of previous results. Numerical examples illustrating absorption of a small vortex by a larger one and a vortex movement across the flow, are direct analogies of the vortex evolution over a hill and a ridge, respectively. At the same time, strong influence of strain drastically changes the vortex structure.  相似文献   

11.
Several theoretical models for the East African Low Level Jet Stream are described. They all share the notion that the northward advection of planetary vorticity across the equator, coupled with the presence of a north-south mountain barrier, leads to the formation of a low-level western boundary current (akin to the Gulf-Stream) along the equatorial east coast of Africa. They differ in the manner in which the planetary vorticity advection is balanced to obtain a quasi-steady state. A purely inertial model predicts the correct cross-stream scale of the jet, but does not reproduce the observed inner shear layer which reduces the jet velocity to zero inland near the highlands. The lateral friction model can produce a realistic jet profile if the horizontal eddy viscosity (appearing as a free parameter) is chosen appropriately. However this solution shows a recirculation, i.e., northerly flow, off the coast that has not yet been observed. Finally, a model that includes bottom friction over variable topography also can give realistic jet profiles. If one accepts that the mountains, the Beta effect, and some form of inertial or frictional acceleration act together to produce the cross-equatorial low level jet stream, then one can formulate the types of observations needed to distinguish between the various theories.  相似文献   

12.
Over the past 30 years, reclamation projects and related changes have impacted the hydrodynamics and sediment transport in the Bohai Sea. Three-dimensional tidal current models of the Bohai Sea and the Yellow Sea were constructed using the MIKE 3 model. We used a refined grid to simulate and analyze the effects of changes in coastline, depth, topography, reclamation, the Yellow River estuary, and coastal erosion on tidal systems, tide levels, tidal currents, residual currents, and tidal fluxes. The simulation results show that the relative change in the amplitude of the half-day tide is greater than that of the full-day tide. The changes in the tidal amplitudes of M2, S2, K1, and O1 caused by coastline changes accounted for 27.76–99.07% of the overall change in amplitude from 1987 to 2016, and water depth changes accounted for 0.93–72.24% of the overall change. The dominant factor driving coastline changes is reclamation, accounting for 99.55–99.91% of the amplitude changes in tidal waves, followed by coastal erosion, accounting for 0.05–0.40% of the tidal wave amplitude changes. The contribution of changes in the Yellow River estuary to tidal wave amplitude changes is small, accounting for 0.01–0.12% of the amplitude change factor. The change in the highest tide level (HTL) is mainly related to the amplitude change, and the correlation with the phase change is small. The dominant factor responsible for the change in the HTL is the tide amplitude change in M2, followed by S2, whereas the influence of the K1 and O1 tides on the change in the HTL is small. Reclamation resulted in a decrease in the vertical average maximum flow velocity (VVAM) in the Bohai Sea. Shallower water depths have led to an increase in the VVAM; deeper water depths have led to a decrease in the maximum flow velocity. The absolute value of the maximum flow velocity gradually decreases from the surface to the bottom, but the relative change value is basically constant. The changes in the tidal dynamics of the Bohai Sea are proportional to the degree of change in the coastline. The maximum and minimum changes in the tidal flux appear in Laizhou Bay (P-LZB) and Liaodong Bay (P-LDB), respectively. The changes in the tidal flux are related to the change in the area of the bay. Due to the reduced tidal flux, the water exchange capacity of the Bohai Sea has decreased, impacting the ecological environment of the Bohai Sea. Strictly controlling the scale of reclamation are important measures for reducing the decline in the water exchange capacity of the Bohai Sea and the deterioration of its ecological environment.  相似文献   

13.
An idealized numerical study of the influence of a tidal flow around an island has been undertaken with ROMS. The study focusses on coastal island wakes which are mainly controlled by elliptical tidal current flows on shallow shelves. This model is typical of some isolated continental shelf islands. The model is forced by a semi-diurnal barotropic inertia gravity wave imposed on the four open boundaries of a rectangular domain and its propagation results in an elliptical tidal flow within the domain in which the circular island lies. The influence of the surrounding island bathymetry and of the ellipse shape has been studied both in two and three dimensions. In the island vicinity, the residual circulation patterns over a tidal period show alongshore flow divergence along the major axis and convergence along the minor axis. A thin tidal ellipse (i.e. with a large ratio between major and minor axes) leads to strong eddy activity periods in the lee of the island during the flood and ebb phases, with eddy dissipation phases in between. By contrast, an almost round ellipse (axis ratio nearly 1) leads to vorticity filaments which continuously progress around the island without eddy shedding. The presence of a topographic slope in the vicinity of the island strengthens the eddy activity. This study suggests that the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy. In three dimensions with a surrounding bathymetry, an intense upwelling occurs in a large area in the lee of the island and the vertical velocities are stronger with thinner ellipses. With a flat bottom the vertical motions are almost fully generated by convergence and divergence of the secondary flow. With a varying bottom topography, the vertical motions come from a combination of this mechanism with convergence and divergence of the depth averaged flow.  相似文献   

14.
The current study deals with a parameterization of diapycnal diffusivity in an ocean model. The parameterization estimates the diapycnal diffusivity depending on the location of tidal-related energy dissipation over rough topography. The scheme requires a bottom roughness map that can be chosen depending on the scales of topographic features. Here, we implement the parameterization on an ocean general circulation model, and we examine the sensitivity of the modeled circulations to different spatial scales of the modeled bottom roughness. We compare three simulations that include the tidal mixing scheme using bottom roughness calculated at three different ranges of spatial scales, with the largest scale varying up to 200?km. Three main results are discussed. First, the dependence of the topographic spectra with depth, characterized by an increase in spectral energy over short length scales in the deep ocean, influences the vertical profile of the diffusivity. Second, the changes in diffusivities lead to different equilibrium solutions in the Atlantic meridional overturning circulation and bottom circulation. In particular, the lower cell of the Atlantic overturning and the bottom water transport in the Pacific Ocean are stronger for stronger diffusivities at the corresponding basins and depths, and the strongest when using the small-scale roughness map. Third, a comparison of the density fields of the three simulations with the density field of World Ocean Atlas dataset, from which the models are initialized, shows that among the simulations with three different roughness maps, the one using small-scale bottom roughness map has the smallest density bias.  相似文献   

15.

The current study deals with a parameterization of diapycnal diffusivity in an ocean model. The parameterization estimates the diapycnal diffusivity depending on the location of tidal-related energy dissipation over rough topography. The scheme requires a bottom roughness map that can be chosen depending on the scales of topographic features. Here, we implement the parameterization on an ocean general circulation model, and we examine the sensitivity of the modeled circulations to different spatial scales of the modeled bottom roughness. We compare three simulations that include the tidal mixing scheme using bottom roughness calculated at three different ranges of spatial scales, with the largest scale varying up to 200 km. Three main results are discussed. First, the dependence of the topographic spectra with depth, characterized by an increase in spectral energy over short length scales in the deep ocean, influences the vertical profile of the diffusivity. Second, the changes in diffusivities lead to different equilibrium solutions in the Atlantic meridional overturning circulation and bottom circulation. In particular, the lower cell of the Atlantic overturning and the bottom water transport in the Pacific Ocean are stronger for stronger diffusivities at the corresponding basins and depths, and the strongest when using the small-scale roughness map. Third, a comparison of the density fields of the three simulations with the density field of World Ocean Atlas dataset, from which the models are initialized, shows that among the simulations with three different roughness maps, the one using small-scale bottom roughness map has the smallest density bias.

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16.
We have performed laboratory experiments using a Hele-Shaw cell to model a saturated, porous layer with various sinusoidal upper boundaries. Our intent was to determine the range of conditions over which boundary topography can control the pattern of thermal convection within a porous layer, and thereby take the first step toward understanding why heat flow seems correlated with hypsography in many areas of the ocean floor.These experiments indicate that above the critical Rayleigh number, topography does not control the convection pattern, except when the topographic wavelength is comparable to the depth of water penetration. Scaled to the depth of the layer, the convective wavenumbers are restricted to values between 2.5 and 4.8—a range which brackets π, the natural wavenumber for convection in a porous slab with planar, isothermal, impermeable boundaries. Topographies within this range control the circulation pattern perfectly, with downwelling under valleys and upwelling aligned with topographic highs. Other topographies do not force the pattern, although in some cases, the convection wavenumber may be a harmonic of the topographic wavenumber. Unforced circulation cells wander and vary in size, because they are not locked to the topography.For these experiments we employed eight different topographies with non-dimensional wavenumbers between 1.43 and 8.17, and we studied the flow at Rayleigh numbers between zero and five times the critical Rayleigh number. The amplitude of each topography tapered linearly (over a factor of three to six) from one end of the apparatus to the other, and the mean topographic amplitude was 0.05 times the depth of the layer. Under these conditions, amplitude has only a minor effect on the structural form and vigor of supercritical convection.Our results may apply to submarine geothermal systems, sealed by a thin layer of impermeable sediment draped over the basement topography. In this case, the convection wavelength—as measured perhaps by the spatial periodicity of conductive heat flow—may be a good measure of the depth to which water penetrates the crust. Where the circulation correlates with the bottom topography, it may be because the topographic wavelength is comparable to the depth to which water penetrates the porous crust.  相似文献   

17.
Abstract

This is a broad survey of the interaction of modons with topography in a one-layer, quasigeostrophic model. Numerical simulations of modons interacting with ridges, hills, random topography and other obstacles are presented. The behavior of the modon is compared to numerical simulations of a two-point-vortex model, which proves a useful guide to the basic trajectory deflection mechanism. Under sufficiently strong but quasigeostrophically valid topographic perturbations, the modon is shown to fission into two essentially independent, oppositely-signed vortices. In the breakup of a modon near a hill it is found that the positive vortex migrates to the top of the hill. The resulting correlation between the positive vorticity trapped over the hill and the topography is in sharp contrast with the theories of turbulent flow over topography and generation of flow over topography by large scale forcing, both of which describe the development of vorticity anticorrelated with topography. A heuristic explanation of this new behavior is provided in terms of the dynamics of β bT-plane vortices. Further, it is found that a modon travelling over rough topography homogenizes the field of potential vorticity in its vicinity. This behavior is explained in terms of the induced eddy activity near the modon.  相似文献   

18.
A new mathematical approach to kinematics and dynamics of planar uniform vortices in an incompressible inviscid fluid is presented. It is based on an integral relation between Schwarz function of the vortex boundary and induced velocity. This relation is firstly used for investigating the kinematics of a vortex having its Schwarz function with two simple poles in a transformed plane. The vortex boundary is the image of the unit circle through the conformal map obtained by conjugating its Schwarz function. The resulting analysis is based on geometric and algebraic properties of that map. Moreover, it is shown that the steady configurations of a uniform vortex, possibly in presence of point vortices, can be also investigated by means of the integral relation. The vortex equilibria are divided in two classes, depending on the behavior of the velocity on the boundary, measured in a reference system rotating with this curve. If it vanishes, the analysis is rather simple. However, vortices having nonvanishing relative velocity are also investigated, in presence of a polygonal symmetry. In order to study the vortex dynamics, the definition of Schwarz function is then extended to a Lagrangian framework. This Lagrangian Schwarz function solves a nonlinear integrodifferential Cauchy problem, that is transformed in a singular integral equation. Its analytical solution is here approached in terms of successive approximations. The self-induced dynamics, as well as the interactions with a point vortex, or between two uniform vortices are analyzed.  相似文献   

19.
Due to the increasing popularity of analyzing empirical Green’s functions obtained from ambient seismic noise, more and more regional tomographical studies based on short-period surface waves are published. Results could potentially be biased in mountainous regions where topography is not small compared to the wavelength and penetration depth of the considered waves. We investigate the effect of topography on the propagation of short-period Rayleigh waves empirically by means of synthetic data using a spectral element code and a 3-D model with real topography. We show that topography along a profile through the studied area can result in an underestimation of phase velocities of up to about 0.7% at the shortest investigated period (3 s). Contrary to the expectation that this bias results from the increased surface distance along topography, we find that this error can be estimated by local topographic contrasts in the vicinity of the receiver alone. We discuss and generalize our results by considering topographic profiles through other mountain ranges and find that southern Norway is a good proxy to assess the topography effect. Nevertheless, topographic bias on phase velocity measurements is in general not large enough to significantly affect recovered velocity variations in the ambient noise frequency range.  相似文献   

20.
A set of 61 normal modes with periods between 7.8 and 133.1 h has been calculated, using a 1° model of the global ocean, including the Arctic Ocean. The model explicitly considers frictional forces and ocean self-attraction and loading effects. The latter effects have generally been taken into account by parameterization, but for some modes the effects have also been considered fully. Due to friction, the computed eigenfrequencies are complex, exhibiting also the varying dissipative properties of the modes and their dependence on the distribution of potential and kinetic energies over the oceanic regions. In detail, gravity modes having periods less then 80 h and dominating the semi-diurnal and the diurnal tides, topographically controlled vorticity modes with periods longer than diurnal, and two planetary vorticity modes with periods of 96.8 and 119.4 h have been identified. These planetary vorticity modes have their energies distributed over Pacific, Atlantic, and Indian Oceans, while the other modes with periods longer than 80 h, as vorticity modes, have their energies concentrated on topographic structures of restricted extension. The modes are discussed with respect to their wave properties, e.g., concerning quasi-standing-wave resonances and to the appearance of Kelvin waves of different orders and trapped by different coastlines. In particular, the relevance of specific modes for the development of the fields of the most important semi-diurnal and diurnal tidal constituents is investigated.  相似文献   

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