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1.
Analytical solution for the tidally induced Lagrangian residual current in a narrow bay 总被引：2，自引：1，他引：1
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
2.
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
3.
Guangliang Liu Zhe Liu Huiwang Gao Zengxiang Gao Shizuo Feng 《Ocean Dynamics》2012,62(10-12):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. 相似文献
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.
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
6.
Abstract Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2. 相似文献
7.
3D analytical solution to the tidally induced Lagrangian residual current equations in a narrow bay 总被引：1，自引：0，他引：1
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
8.
Net sediment transport in tidal basins: quantifying the tidal barotropic mechanisms in a unified framework 总被引：1，自引：1，他引：0
Vincenzo Marco Gatto Bram Christiaan van Prooijen Zheng Bing Wang 《Ocean Dynamics》2017,67(11):1385-1406
Net sediment transport in tidal basins is a subtle imbalance between large fluxes produced by the flood/ebb alternation. The imbalance arises from several mechanisms of suspended transport. Lag effects and tidal asymmetries are regarded as dominant, but defined in different frames of reference (Lagrangian and Eulerian, respectively). A quantitative ranking of their effectiveness is therefore missing. Furthermore, although wind waves are recognized as crucial for tidal flats’ morphodynamics, a systematic analysis of the interaction with tidal mechanisms has not been carried out so far. We review the tide-induced barotropic mechanisms and discuss the shortcomings of their current classification for numerical process-based models. Hence, we conceive a unified Eulerian framework accounting for wave-induced resuspension. A new methodology is proposed to decompose the sediment fluxes accordingly, which is applicable without needing (semi-) analytical approximations. The approach is tested with a one-dimensional model of the Vlie basin, Wadden Sea (The Netherlands). Results show that lag-driven transport is dominant for the finer fractions (silt and mud). In absence of waves, net sediment fluxes are landward and spatial (advective) lag effects are dominant. In presence of waves, sediment can be exported from the tidal flats and temporal (local) lag effects are dominant. Conversely, sand transport is dominated by the asymmetry of peak ebb/flood velocities. We show that the direction of lag-driven transport can be estimated by the gradient of hydrodynamic energy. In agreement with previous studies, our results support the conceptualization of tidal flats’ equilibrium as a simplified balance between tidal mechanisms and wave resuspension. 相似文献
9.
In this paper, a new particle image velocimetry (PIV)-based measurement method is proposed to obtain the high-resolution tide-induced Lagrangian residual current field in the laboratory. A long gravity wave was generated to simulate the tide in a narrow tank full of water laden with PIV particles. Consecutive charge-coupled device (CCD) images were recorded with the studied layer illuminated with a laser beam. Two images separated by one tidal period were processed by applying the pattern-matching algorithm to get the horizontal tide-induced Lagrangian residual current field. The results coincide with sporadic results from the traditional surface-float tracing method, but with much higher spatial resolution and accuracy. Furthermore, it is found that the direct acquisition of the Lagrangian residual current may reduce the error at least by one order compared with those acquisition methods that require the detailed information of the tidal cycle.
相似文献10.
Alexander M. krigel 《地球物理与天体物理流体动力学》2013,107(3):213-223
Abstract Friedmann's equation and the potential vorticity equation are generalised for turbulent motion. The generalised equations incorporate some new phenomena connected with turbulent transport of mass. It is proved that, if ?×[S×Ω+S(?·S)]≠0 where Ω is the absolute vorticity of the velocity and S is the turbulent density flux, then the Helmholtz-Kelvin theorem concerning the conservation of the velocity circulation around a closed path is violated and the potential vorticity is not a Lagrangian adiabatic invariant. The effects of this turbulent transport of mass on the creation or dissipation of vorticity discussed here is not equivalent to effects of baroclinicity or viscosity. Some possible implications of the new circulation theorem in geophysical and astrophysical fluid dynamics are discussed. 相似文献
11.
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
12.
Andrew Lane 《Ocean Dynamics》2005,55(5-6):541-548
The development and application of a Lagrangian particle-tracking model to simulate sediment transport in the Mersey Estuary
(UK) is described. Each of the particles (up to a million in total) is advected horizontally by the 3-D tidal currents. Related
vertical movements are: (1) downwards by settlement at a prescribed velocity w
s and (2) both upwards and downwards by a distance related to the vertical eddy diffusivity. In a novel departure from traditional
practice, where initial distributions of surficial sediments are specified, all particles are introduced at the seaward boundary
of the model. Provenance studies indicate surficial sediments are overwhelmingly of marine origin. For the predominant fine
sediments, ‘cyclical convergence’ in suspended sediment concentrations is approximated after about two spring-neap tidal cycles.
Comparisons are shown between the suspended sediment concentrations and net deposition rates computed by this model against
observed values and earlier computations utilising both 1-D and 3-D Eulerian models. While all of these results are in broad
agreement, the flexibility of the Lagrangian approach for simulating flocculation, consolidation and mixed sediments illustrates
its future potential. 相似文献
13.
Ocean Dynamics - The 3D Lagrangian residual velocity (LRV) is solved analytically in a narrow bay employing a vertically varying eddy viscosity coefficient. The nondimensional vertical profile of... 相似文献
14.
Mechanisms of along-channel sediment transport in the North Passage of the Yangtze Estuary and their response to large-scale interventions 总被引：4，自引：0，他引：4
The effects of large-scale interventions in the North Passage of the Yangtze Estuary (the Deep Waterway Project, DWP) on the along-channel flow structure, suspended sediment distribution and its transport along the main channel of this passage are investigated. The focus is explaining the changes in net sediment transport in terms of physical mechanisms. For this, data of flow and suspended sediment concentration (SSC), which were collected simultaneously at several locations and at different depths along the main channel of the North Passage prior to and after the engineering works, were harmonically analyzed to assess the relative importance of the transport components related to residual (time-mean) flow and various tidal pumping mechanisms. Expressions for main residual flow components were derived using theoretical principles. The SSC revealed that the estuarine turbidity maximum (ETM) was intensified due to the interventions, especially in wet seasons, and an upstream shift and extension of the ETM zone occurred. The amplitude of the M 2 tidal current considerably increased, and the residual flow structure was significantly altered by engineering works. Prior to the DWP, the residual flow structure was that of a gravitational circulation in both seasons, while after the DWP, there was seaward flow throughout the channel during the wet season. The analysis of net sediment transport reveals that during wet seasons and prior to the DWP, the sediment trapping was due to asymmetric tidal mixing, gravitational circulation, tidal rectification, and M 2 tidal pumping, while after the DWP, the trapping was primarily due to seaward transport caused by Stokes return flow and fresh water discharge and landward transport due to M 2 tidal pumping and asymmetric tidal mixing. During dry seasons, prior to the DWP, trapping of sediment at the bottom relied on landward transports due to Stokes transport, M 4 tidal pumping, asymmetric tidal mixing, and gravitational circulation, while after the DWP the sediment trapping was caused by M 2 tidal pumping, Stokes transport, asymmetric tidal mixing, tidal rectification, and gravitational circulation. 相似文献
15.
Tidal circulation in Cobscook Bay, a macro tidal basin, is simulated using the three-dimensional, nonlinear, finite element
ocean model, QUODDY_dry. Numerical particles are released from various transects in the bay at different tidal phases and tracked for several tidal
cycles. Initially, nearby particles in the main tidal channel experience a great deal of spreading and straining, and after
a few tidal cycles, they are separated in different parts of the bay. The fundamental mechanism for particle dispersion is
the chaotic advection that arises from long tidal excursions passing through many residual eddies. A loosely correlated, inverse
relationship between the two dimensionless parameters, ν (the ratio of the residual current to the tidal current) and λ (the ratio of the tidal excursion to the main topographic scale), can be constructed for large values of ν. Several Lagrangian statistical measures are used to quantify and distinguish dispersion regimes in different parts of Cobscook
Bay. It is found that the effective Lagrangian dispersion coefficient can be estimated using the product of the magnitude
of residual currents and the tidal excursion. 相似文献
16.
Ocean Dynamics - The nonlinear effect of the summer southeast wind and density on the 3D structures of the full Lagrangian residual velocity (LRV) was quantified for a generally nonlinear system,... 相似文献
17.
Tidal residual eddies are one of the important hydrodynamic features in tidally dominant estuaries and coastal bays, and they could have significant effects on water exchange in a tidal system. This paper presents a modeling study of tides and tidal residual eddies in Puget Sound, a tidally dominant fjord-like estuary in the Pacific Northwest coast, using a three-dimensional finite-volume coastal ocean model. Mechanisms of vorticity generation and asymmetric distribution patterns around an island/headland were analyzed using the dynamic vorticity transfer approach and numerical experiments. Model results of Puget Sound show that a number of large twin tidal residual eddies exist in the Admiralty Inlet because of the presence of major headlands in the inlet. Simulated residual vorticities near the major headlands indicate that the clockwise tidal residual eddy (negative vorticity) is generally stronger than the anticlockwise eddy (positive vorticity) because of the effect of Coriolis force. The effect of tidal residual eddies on water exchange in Puget Sound and its subbasins was evaluated by simulations of dye transport. It was found that the strong transverse variability of residual currents in the Admiralty Inlet results in a dominant seaward transport along the eastern shore and a dominant landward transport along the western shore of the inlet. A similar transport pattern in Hood Canal is caused by the presence of tidal residual eddies near the entrance of the canal. Model results show that tidal residual currents in Whidbey Basin are small in comparison to other subbasins. A large clockwise residual circulation is formed around Vashon Island near entrance of South Sound, which can potentially constrain the water exchange between the Central Basin and South Sound. 相似文献
18.
In this paper, a new particle image velocimetry (PIV)-based measurement method is proposed to obtain the high-resolution tide-induced Lagrangian residual current field in the laboratory. A long gravity wave was generated to simulate the tide in a narrow tank full of water laden with PIV particles. Consecutive charge-coupled device (CCD) images were recorded with the studied layer illuminated with a laser beam. Two images separated by one tidal period were processed by applying the pattern-matching algorithm to get the horizontal tide-induced Lagrangian residual current field. The results coincide with sporadic results from the traditional surface-float tracing method, but with much higher spatial resolution and accuracy. Furthermore, it is found that the direct acquisition of the Lagrangian residual current may reduce the error at least by one order compared with those acquisition methods that require the detailed information of the tidal cycle. 相似文献
19.
An idealized numerical model is developed to study the spatial asymmetry of ebb–tidal deltas under influence of large-scale alongshore tidal currents. It is shown that the asymmetry of the delta depends on the magnitude of the cross-shore and large scale alongshore tidal currents, their phase difference, and on the width of the inlet. Model results are compared with observations of ebb–tidal deltas of the tidal inlet systems of the Dutch Wadden Sea and with the ebb–tidal delta of the Eastern Scheldt, located in the southwestern part of the Netherlands. The modeled current and residual sediment transport patterns agree well with observed ones. The modeled asymmetry of the ebb–tidal delta also agree with observed ones. Furthermore, bottom patterns are consistent with those found with a previous version of the idealized model which focused on the modeling of symmetric ebb–tidal deltas. However, the model is not able to reproduce the observed ebb-dominated channel. The underlying physical processes are explained in terms of vorticity dynamics. The convergence of the mean vorticity flux generates mean vorticity and thereby residual circulation. An analysis shows there is competition between two contributions to the convergence of the mean vorticity flux. This competition explains the sensitivity of the results to the model parameters. 相似文献
20.
Both Eulerian and Lagrangian reactive transport simulations in natural media require selection of a parameter that controls the “promiscuity” of the reacting particles. In Eulerian models, measurement of this parameter may be difficult because its value will generally differ between natural (diffusion-limited) systems and batch experiments, even though both are modeled by reaction terms of the same form. And in Lagrangian models, there previously has been no a priori way to compute this parameter. In both cases, then, selection is typically done by calibration, or ad hoc. This paper addresses the parameter selection problem for Fickian transport by deriving, from first principles and D (the diffusion constant) the reaction-rate-controlling parameters for particle tracking (PT) codes and for the diffusion–reaction equation (DRE). Using continuous time random walk analysis, exact reaction probabilities are derived for pairs of potentially reactive particles based on D and their probability of reaction provided that they collocate. Simultaneously, a second PT scheme directly employing collocation probabilities is derived. One-to-one correspondence between each of D, the reaction radius specified for a PT scheme, and the DRE decay constant are then developed. These results serve to ground reactive transport simulations in their underlying thermodynamics, and are confirmed by simulations. 相似文献