Depth-averaged Flow Research Articles

Hydrodynamic variability along a low-energy estuarine beach located in an open estuary

A process-based modelling study was carried out by applying a depth-averaged flow module (MIKE 21 HD) and a spectral wave model (MIKE 21 SW) to examine near-shore hydrodynamics of an estuarine beach located in an open estuary: Jimmy’s Beach, Port Stephens, Australia. The models were calibrated and validated against recently acquired hydrodynamic data. Model results indicate a significant spatial variability in the near-shore wave parameters along the beach, depending on shoreline orientation; proximity to the mouth of the estuary and sheltering influences of adjacent headlands. Local bathymetry and shoreline orientation play a major role in determining the near-shore ocean wave characteristics at a site along the beach. The shoal previously thought to focus higher wave energy into the erosion spot, in contrast, results in wave energy dissipation. Locally generated waves by the prevailing westerly winds at Jimmy’s Beach have low wave energy. Model results also suggest that the near-shore flow patterns are complex due to the presence of tidal eddies and variations in the near-shore wave field along the beach. Currents generated by local wind waves are subordinate to wind stress induced currents. These spatial differences reflect the complex configuration of estuarine shorelines, local topographic controls and variations in exposure to each of the forcing, and may contribute to a high level of beach mobility.

Barotropic and Baroclinic M2 Tides in the Monterey Bay Region

Abstract A high-resolution (250 m) primitive equation model is used to simulate the depth-averaged and baroclinic M2 tides in the Monterey Bay region. The model shows a high level of skill in comparisons with sea level observations. ADCP current observations within the submarine canyon are reasonably well reproduced. The modeled depth-averaged currents have a complex spatial pattern with magnitudes in excess of 0.1 m s−1 near Moss Landing. During the second half of flood (ebb) tide, the flow is into (out of) the bay through the canyon but out of (into) the bay over the shelf regions. This depth-averaged flow pattern is not evident in a diagnostic run, implying a feedback between the internal tides and the pressure gradient in the bay. The depth-integrated baroclinic (total minus depth-averaged) energy fluxes show a complex beamlike pattern due to the interaction of energy from multiple sources. The beams have magnitudes up to 1 kW m−1 interspersed with regions of near-zero depth-integrated flux. Energy entering the bay propagates northward from generation regions along the continental margins to the south of the bay (notably on the flanks of Sur Platform) and is steered into the canyon. A localized increase in depth-integrated baroclinic flux magnitude (up to 5 times the values elsewhere in the domain) closely follows the canyon axis near the mouth of the bay, presumably due to topographic focusing. Upper ocean velocities from a long-term surface mooring (MBARI M1) are used to assess the temporal variability of the M2 tide outside the canyon.

Validation of volume continuity method for estimation of cross-shore swash flow velocity

The use of flow volume continuity to estimate depth-averaged cross-shore swash flow velocity is validated using appropriate field data. Swash surface and beach face elevation were measured by a network of ultrasonic altimeters mounted through the swash zone of a sandy beach. Estimates of cross-shore flow velocity derived from these data compare well with concurrent measurements obtained from a vertical array of four electromagnetic current meters (EMCMs). Significantly, the continuity technique allows swash velocity to be estimated throughout the full swash cycle. This is not possible using fixed current meters and the new measurements indicate that swash velocity is more negatively skewed than previously observed.

Computations of suspended sediment transport in a shallow side-cavity using depth-averaged 2D models with effects of secondary currents

Two-dimensional (2D) depth-averaged shallow flow models’ integrated effects of secondary currents are applied to open channel flows with a side cavity, and the accuracy of predictions of the flow structures as well as the behavior of suspended sediment transport is examined. The flow in a side-cavity is characterized by formations of a steady recirculation with a vertical axis and associated secondary current due to a centrifugal force (a secondary current of the first kind). The flow structures become completely three-dimensional and suspended sediment transports are affected by such complicated flow features. In this study, we applied depth-averaged shallow flow equations including effects of secondary currents, instead of 3D flow equations considering computational efficiency. We applied 4 different types of models for shallow flow equations and compared the performances of each model. First, these models were applied to a simple flow in a torus-shape channel with rigidly rotating flow, in order to consider the fundamental characteristics of suspended sediment transport. Then the models were applied to open channel flows with a rectangular side cavity, in order to consider both flow structures and sediment transport affected by the secondary current. The computations were performed under the same conditions of the laboratory tests and applicability of each model was discussed through the comparison between computational and experimental results. The model considering the lag of development of secondary current behind the streamline curvature, and the deformation of mean velocity profiles affected by secondary currents showed excellent performance for predicting flow phenomena with recirculation.

Identification of contaminant point source in surface waters based on backward location probability density function method

A backward location probability density function (BL-PDF) method capable of identifying location of point sources in surface waters is presented in this paper. The relation of forward location probability density function (FL-PDF) and backward location probability density, based on adjoint analysis, is validated using depth-averaged free-surface flow and mass transport models and several surface water test cases. The solutions of the backward location PDF transport equation agreed well to the forward location PDF computed using the pollutant concentration at the monitoring points. Using this relation and the distribution of the concentration detected at the monitoring points, an effective point source identification method is established. The numerical error of the backward location PDF simulation is found to be sensitive to the irregularity of the computational meshes, diffusivity, and velocity gradients. The performance of identification method is evaluated regarding the random error and number of observed values. In addition to hypothetical cases, a real case was studied to identify the source location where a dye tracer was instantaneously injected into a stream. The study indicated the proposed source identification method is effective, robust, and quite efficient in surface waters; the number of advection–diffusion equations needed to solve is equal to the number of observations.

Alternative depth-averaged models for gravity currents and free shear flows

Two approaches have traditionally been used to describe the widening rate of jets and plumes: the diffusion concept of Prandtl, and the entrainment principle of Morton, Taylor and Turner. The entrainment concept is based on depth-averaged flow scales, and was later applied to plane gravity currents on an incline by Ellison and Turner [ET]. The two parameterizations are compared here for free shear flows, and gravity currents. It is shown that the diffusion concept is suitable for supercritical gravity currents, and that both approaches agree for subcritical ones. Depth-averaged models are also used for open channel flows, but the depth and velocity scales for the two flows are different. Those of ET are derived from the velocity distribution, whereas the depth of an open channel flow is the vertical extent of the dense liquid phase, and the velocity is derived from its flux. To reconcile the two descriptions, we extended the mass-based flow scales of open channel flows to gravity currents in an earlier contribution. In the present study these scales are outlined, and extended further to axisymmetric and non-buoyant free shear flows. Ratios of the diffusion rates in terms of mass- and velocity-based flow scales, are obtained from available experimental data for free shear flows.

CHARACTERISTICS OF THE INTERNAL TIDE AND ITS ASSOCIATED COOLING SYSTEM IN GENKA BAY, OKINAWA, JAPAN

Profiling and mooring measurements were carried out in Genka Bay, Okinawa, Japan to study the characteristics of the internal tidal current and its associated cooling system. The study results show that the depth-averaged current flows nearly parallel to the coastline. There is also an existence of a cross-shore internal tidal current according to the vertical structure of the horizontal current. This current influences on the bottom water temperature transmission from offshore to nearshore bottom water and changes the vertical temperature profile even of nearshore regions and thereby establishes a unique cooling system. Spectra of the baroclinic and bottom water temperature also congruent the internal tide based cooling system in GB.

Development of Storm Surge and High Wave-Induced Inundation Model Considering Influence of High Wave and Its Accuracy Validation

A storm surge and high wave-induced inundation model was developed in this study, which consists of the Myers-based typhoon model, a depth-averaged flow model with an one-way nesting method, the wave model SWAN and an inundation flow model using a CIP method. The influence of high wave on storm surge and inundation flow was taken into account by adding the half value of the siginificant wave height obtained from the SWAN to storm surge fields at each time step. The validity of the model was verified by comparing with the experimental result of flood inudation due to dam break and the observation data of storm surge and inundation induced by Ise bay typhoon.

RMA2/RMA4 모형을 이용한 서낙동간 수문연계운영의 수질개선 효과 예측

An objective of this study is as follows: 1) performing sensitivity analysis and parameter estimation of RMA2 and RMA4 models for the West-Nakdong River, 2) drawing up alternatives of gates-operation for water-quality enhancement, and 3) quantitative evaluation of methodology of 'flow-restoration by gates-operation' among 'Comprehensive Plan Improving Water-Quality in the West-Nakdong River(WNR)' with the target water-quality(BOD at Nakbon-N point: below 4.3 mg/L). The parameters for the RMA2 (depth-averaged two-dimensional flow model) and RMA4 (depth-averaged two-dimensional water-quality model) were determined by sensitivity analysis. Result of parameter estimation for RMA2 and RMA4 models is <TEX>$1,000\;Pa{\cdot}s$</TEX> of the eddy viscosity, 20 of the Peclet number, 0.025 of the Manning coefficient, and <TEX>$1.0\;m^2/s$</TEX> of the diffusion coefficient. We have evaluated the effects of water-quality enhancement of the selected alternatives by numerical simulation technique with the models under the steady-state flow condition and the time-variant transport condition. Because of no-resuspension from river bottom and considering BOD as conservative matter, these simulation results slightly differ from real phenomena. In the case of <TEX>$50\;m^3/s$</TEX> of Daejeo-gate inflow, two-dimensional flow pn results result represents that small velocity occurs in the Pyungkang Stream and no flow in the Maekdo River. In the WNR, there occurs the most rapid flow near timhae-bridge. In the WNR, changes of water-quality for the four selected simulation cases(6, 10, 30, <TEX>$50\;m^3/s$</TEX> of the Daejeo-gate inflow) were predicted. Since the Daejeo-Gate and the Noksan-Gate can be opened up to 7 days, it would be found that sustainable inflow of <TEX>$30\;m^3/s$</TEX> at the Daejeo-gate makes BOD in the WNR to be under the target of water-quality.

Evaluation of total load sediment transport formulas using ANN

The calculated results from various sediment transport formulas often differ from each other and from measured data. Some parameters in the sediment transport formulas are more effective than others to estimate total sediment load. In this study, an Artificial Neural Network (ANN) model is trained using four dominant parameters of sediment transport formulas. ANN models are able to reveal hidden laws of natural phenomena such as sediment transport process. The results of ANN and some total bed material load sediment transport formulas have been compared to indicate the importance of variables which can be used in developing sediment transport formulas. To train ANN, average flow velocity, water surface slopes, average flow depth, and median particle diameter are used as dominant parameters to estimate total bed material load. Two hundreds and fifty samples are used to train the ANN model. Twenty-four sets of field data not used in the training nor calibration of ANN are used to compare or verify the accuracy of ANN and some well-known total bed material load formulas. The test results show that the ANN model developed in this study using minimum number of dominant factors is a reliable and uncomplicated method to predict total sediment transport rate or total bed material load transport rate. Results show that the accuracy of formulas in descending order are those by Yang (1973), Laursen (1958), Engelund and Hansen (1972), Ackers and White (1973), and Toffaleti (1969). These results are similar to those made by ASCE (1982) based on laboratory and field data not used in this paper. Study results also show that the formulas based on physical laws of sediment transport, like those formulas that were developed based on power concept, are more accurate than other formulas for estimating total bed material sediment load in rivers.

Two-Dimensional Depth-Averaged Flow Modeling with an Unstructured Hybrid Mesh

An unstructured hybrid mesh numerical method is developed to simulate open channel flows. The method is applicable to arbitrarily shaped mesh cells and offers a framework to unify many mesh topologies into a single formulation. A finite-volume discretization is applied to the two-dimensional depth-averaged equations such that mass conservation is satisfied both locally and globally. An automatic wetting-drying procedure is incorporated in conjunction with a segregated solution procedure that chooses the water surface elevation as the main variable. The method is applicable to both steady and unsteady flows and covers the entire flow range: subcritical, transcritical, and supercritical. The proposed numerical method is well suited to natural river flows with a combination of main channels, side channels, bars, floodplains, and in-stream structures. Technical details of the method are presented, verification studies are performed using a number of simple flows, and a practical natural river is modeled to il...

Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part I: Modeling Flow over Idealized Symmetric Banks

Abstract This study examines how coastal banks influence wind-driven circulation along stratified continental shelves. Numerical experiments are conducted for idealized symmetric banks; the standard bank (200 km long and 50 km wide) has dimensions similar to the Heceta Bank complex along the Oregon shelf. Model runs are forced with 10 days of steady winds (0.1 Pa); upwelling and downwelling cases are compared. The bank introduces significant alongshelf variability in the currents and density fields. Upwelling-favorable winds create an upwelling front and a baroclinic jet (flowing opposite coastal-trapped wave propagation) that bend around the standard bank, approximately centered on the 90-m isobath. The upwelling jet is strongest over the upstream bank half, where it advects a tongue of dense water over the bank. There is a current reversal shoreward of the main jet at the bank center. Upwelling is most intense over the upstream part of the bank, while there is reduced upwelling and even downwelling over other bank sections. Downwelling-favorable winds create a near-bottom density front and a baroclinic jet (flowing in the direction of coastal-trapped wave propagation) that bend around the standard bank; the jet core moves from the 150-m isobath to the 100-m isobath and back over the bank. The downwelling jet is slowest and widest over the bank; there are no current reversals. Results over the bank are more similar to 2D results (that preclude alongshelf variability) than in the upwelling case. Downwelling is weakened over the bank. The density field evolution over the bank is fundamentally different from the upwelling case. Most model results for banks with different dimensions are qualitatively similar to the standard run. The exceptions are banks having a radius of curvature smaller than the inertial radius; the main jet remains detached from the coast far downstream from these banks. The lowest-order across-stream momentum balance indicates that the depth-averaged flow is geostrophic. Advection, ageostrophic pressure gradients, wind stress, and bottom stress are all important in the depth-averaged alongstream momentum balance over the bank. There is considerable variability in alongstream momentum balances over different bank sections. Across-shelf and alongshelf advection both change the density field over the bank. Barotropic potential vorticity is not conserved, but the tendency for relative vorticity changes and depth changes to partially counter each other results in differences between the upwelling and downwelling jet paths over the bank. Only certain areas of the bank have significant vertical velocities. In these areas of active upwelling and downwelling, vertical velocities at the top of the bottom boundary layer are due to either the jet crossing isobaths or bottom Ekman pumping.

Modeling Floating Objects at River Structures

More than half of the commercially navigable waterways in the United States are adversely impacted at some time by ice and debris conditions that hinder operation and delay navigation. This paper describes a method of combining a depth-averaged two-dimensional flow model and a discrete element model customized to simulate floating objects such as ice and debris. The flow model is the shallow-water equation module of the adaptive hydraulics system. The discrete element model (DEM) is based on a method that has been used to simulate river ice and debris accumulations and vessels such as barges. The modeling system provides designers of hydraulic structures, bridges, and ice control structures, a physically based method to evaluate design alternatives in dealing with problems due to the presence of floating objects. Descriptions of the flow model and the DEM are presented, and then numerical applications are provided, demonstrating the modeling of debris passage at the Harlan Diversion Tunnel and the evaluation of navigation conditions attributed to the guard wall at the Greenup Locks and Dam.

ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows

We develop a new family of well-balanced path-conservative quadrature-free one-step ADER finite volume and discontinuous Galerkin finite element schemes on unstructured meshes for the solution of hyperbolic partial differential equations with non-conservative products and stiff source terms. The fully discrete formulation is derived using the recently developed framework of explicit one-step P N P M schemes of arbitrary high order of accuracy in space and time for conservative hyperbolic systems [Dumbser M, Balsara D, Toro EF, Munz CD. A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes. J Comput Phys 2008;227:8209–53]. The two key ingredients of our high order approach are: first, the high order accurate P N P M reconstruction operator on unstructured meshes, using the WENO strategy presented in [Dumbser M, Käser M, Titarev VA Toro EF. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J Comput Phys 2007;226:204–43] to ensure monotonicity at discontinuities, and second, a local space–time Galerkin scheme to predict the evolution of the reconstructed polynomial data inside each element during one time step to obtain a high order accurate one-step time discretization. This approach is also able to deal with stiff source terms as shown in [Dumbser M, Enaux C, Toro EF. Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J Comput Phys 2008;227:3971–4001]. These two key ingredients are combined with the recently developed path-conservative methods of Parés [Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300–21] and Castro et al. [Castro MJ, Gallardo JM, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. Math Comput 2006;75:1103–34] to treat the non-conservative products properly. We show applications of our method to the two-layer shallow water equations as well as applications to the recently published depth-averaged two-fluid flow model of Pitman and Le [Pitman EB, Le L. A two-fluid model for avalanche and debris flows. Philos Trans Roy Soc A 2005;363:1573–601].

A Phase Diagram for Turbulent, Transitional, and Laminar Clay Suspension Flows

Abstract New phase diagrams for the dynamic structure of clay-laden open-channel flows are proposed. These diagrams can be used to distinguish between turbulent Newtonian, transitional, and laminar non-Newtonian flow behavior, on the basis of the balance between turbulent forces (approximated by the horizontal components of flow velocity and turbulence intensity) and cohesive forces (approximated by the suspended clay concentration and rheology). Stability regimes for five different flow types are defined using a comprehensive series of laboratory flume experiments at depth-averaged flow velocities ranging from 0.13 m s−1 to 1.47 m s−1, and at volumetric kaolinite clay concentrations ranging from 0.03% (= 0.8 g L−1) to 16.7% (= 434 g L−1). As clay concentration increases, five flow types can be distinguished: turbulent flow, turbulence-enhanced transitional flow, lower and upper transitional plug flow, and quasi-laminar plug flow. The turbulent properties of transitional flows are shown to be considerably more complex than the common notion of gradual turbulence damping. Turbulence-enhanced transitional flows display higher turbulence intensity than turbulent flows of similar velocity, with such enhancement originating from development of a highly turbulent basal internal shear layer within ~ 0.01 m of the bed. In lower transitional plug flows, the basal internal shear layer separates a lower region of high vertical gradient in horizontal velocity and strong turbulence from an upper region of plug flow with a much gentler velocity gradient and lower turbulence intensity. Kelvin-Helmholtz shear instabilities within the highly turbulent shear layer are expressed as distinct second-scale oscillations in the time series of downstream velocity. Turbulence damping dominates upper transitional plug flows, because strong cohesive forces, inferred to be caused by gelling of the high-concentration clay suspension, start to outbalance turbulent forces. In quasi-laminar plug flows, gelling is pervasive and turbulence is fully suppressed, apart from some minor residual turbulence near the base of these flows. With very few exceptions, all flows pass through the same development stages as clay concentration increases, regardless of their velocity, but the threshold concentrations for turbulence enhancement, gelling, and development of internal shear layers and plug flows are proportional to flow velocity. At flow velocities below ~ 0.5 m s−1, only low concentrations (< 0.75%) of kaolinite are required to induce transitional flow behavior, thus potentially affecting many slow-moving and decelerating clay flows in natural sedimentary environments. However, at flow velocities above 1 m s−1, clay concentrations of at least 6% are required in order for flows to enter the transitional flow phase, but even at these velocities the transitional flow phases make up a significant proportion of the flow phase space. By converting the experimental data to nondimensional Froude number (momentum term) and Reynolds number (cohesive term), it is shown that each boundary between the turbulent, transitional, and laminar flow phases can be described by a specific narrow range of Reynolds numbers. Within the duration of the experiments, settling of clay particles occurred only in plug flows of low flow velocity (and low Froude number), when the flows lacked the strength to support the entire clay suspension load.

Inferring Propagation Direction of Nonlinear Internal Waves in a Vertically Sheared Background Flow

Abstract Internal waves heave the background flow through which they propagate. If the background flow is vertically sheared, the high-pass-filtered velocity field will thus contain signals of both the wave velocity and the heaved flow. Under conditions of large wave amplitude and large background shear—a common situation for nonlinear internal waves in coastal waters—the velocity fluctuations caused by wave heaving of the background flow can be comparable to the wave velocity itself. This complicates the inference of wave properties such as energy flux and propagation direction. The present study deals with methods to infer propagation direction in such situations. Attention is given to three methods that may be applied to acoustic Doppler current profiler measurements: a “filtering” method that estimates wave signals from high-pass-filtered time series, a “beamwise” method that infers wave direction from lagged correlations of echo intensity between the spatially separated acoustic beams of the profiler, and a “modal” method that separates background and wave signals by regressing the high-pass-filtered velocity field onto a normal-mode wave model. The methods are tested using synthetic datasets. The results suggest that the filtering method is biased by wave heaving of the background shear, while the beamwise and modal methods are resistant to heaving. The beamwise method provides accurate predictions of wave propagation angle for cases in which the measurements have high temporal resolution and the environment exhibits no depth-averaged background flow. The limitation on depth-averaged flow is relaxed for the modal method, but it requires the measurement of stratification. These issues are illustrated, and the applicability of these methods is explored with a series of sensitivity tests, and it is found that the different methods perform well under different circumstances.

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.

A novel application of a multi-objective evolutionary algorithm in open channel flow modelling

The Shiono and Knight method (SKM) is a simple depth-averaged flow model, based on the RANS equations which can be used to estimate the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels with the minimum of computational effort. However, in order to apply the SKM, detailed knowledge relating to the lateral variation of the friction factor (f), dimensionless eddy viscosity (λ) and a sink term representing the effects of secondary flow (Γ) are required. In this paper a multi-objective evolutionary algorithm is used to study the lateral variation and value of these parameters for simple trapezoidal channels over a wide range of aspect ratios through the model calibration process. Based on the available experimental data, four objectives are selected and the NSGA-II algorithm is applied to several datasets. The best answer for each set is then selected based on a proposed methodology. Rules relating f, λ and Γ to the wetted parameter ratio (Pb/Pw) for a variety of situations have been developed which provide practical guidance for the engineer on choosing the appropriate parameters in the SKM model.

Discontinuous Galerkin finite element method for shallow two-phase flows

We present a discontinuous Galerkin finite element method for a depth-averaged two-phase flow model. This model contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. [S. Rhebergen, O. Bokhove, J.J.W. van der Vegt, Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, J. Comput. Phys. 227 (2008) 1887]. The goal is to qualitatively validate the model against a laboratory experiment and to show the abilities of the model to capture physical phenomena. To be able to perform these test cases, a WENO slope limiter is investigated in conjunction with a discontinuity detector to detect regions where spurious oscillations appear.

A diagnostic calculation of the circulation in the upper and middle layers of the Luzon Strait and the northern South China Sea during March 1992

Wind data from NCEP and hydrographic data obtained during 8–27 March 1992 have been used to compute circulation in the Luzon Strait and the northern South China Sea using three-dimensional diagnostic models with a modified inverse method. Numerical results are as follows: the main Kuroshio is located above 800 m levels. It has two intrusive branches of the Kuroshio in the areas above 400 m. One part intrudes anti-cyclonically northwestward, then flows through the area above 200 m southwest of Taiwan and into the Taiwan Strait. The other part intrudes westward and flows cyclonically in the areas north of the cyclonic eddies, then flows southward through the southern boundary of the region. The net westward volume transport (VT) through Section at 120°15′E between Luzon Island and Taiwan Island is about 3.0 Sv, net northward VT through northern boundaries into the Taiwan Strait is about 1.4 Sv and net southward VT through southern boundaries is about 1.6 Sv, which finally flows into the Karimata and Mindoro Straits. In the areas above 400 m east of 117°15′E, the circulation is mainly dominated by the basin-scale cyclonic gyre, which consists of two cyclonic eddies. However, in the areas below 400 m east of 119°00′E, the circulation is mainly dominated by basin-scale anti-cyclonic gyre. The joint effect of baroclinity and relief and interaction between wind stress and relief are important in different area respectively for the pattern of the depth-averaged flow across contours of fH −1.