Modelling the three-dimensional tidal flow structure in semi-enclosed basins (original) (raw)

Hydraulic modelling of tidal circulation and flushing in coastal basins

The Paper highlights the increasing concern of planners and designers for the hydroenvironmental problems relating to tidal circulation and flushing in small coastal basins, harbours, and marinas, and the use of physical and mathematical models as design tools to address such problems. Details are given of techniques frequently adopted in using both physical and mathematical models to quantify tidal flow patterns and water exchange characteristics of harbours and marinas. Emphasis is placed on comparative studies where alternative basin geometries and/or bathymetries are proposed. Advantages and disadvantages of both modelling techniques are considered. An example application of each approach is presented. The main purpose of the two studies was to investigate effects of basin geometries on the tidal flow and flushing features for two specific sites-one in the USA, the other in the UK. Results of both studies are reported, together with an interpretation of the data and a summary of the findings. Notatioo C , initial spatial average tracer concentration for volume considered C, spatial average tracer concentration for same volume after n tides E average per cycle exchange coeflicient n number of tides of simulation R average per cycle retention coeflicient T P R tidal prism ratio

Refined flow modelling in coastal areas

WIT Transactions on the Built Environment, 1970

Problems raised by the computation of tidal flows in coastal areas are reviewed. The main factors which are occasionally overlooked are the tidegenerating force and the mean sea level. The effect of some numerical parameters, including parameter estimation of bottom friction are also discussed.

Modelling of Flow in a Tidal Flat Area in the South-Eastern German Bight

This paper sums up the development phases of a flow model for a tidally-dominated area of the German North Sea. The study area is the Dithmarschen Bight located between the Elbe and Eider estuaries. The model presented is a two-dimensional depth-integrated flow model based on the DELFT3D Modelling System developed by Delft Hydraulics in the Netherlands. A description of model set-up as well as the results of sensitivity studies and model calibration and validation procedures are outlined in this contribution. Measurements of water levels and current velocities with a dense spatial and temporal coverage were used for this purpose. It was found that hydrodynamic forcing along the open sea boundaries is by far the most important factor governing the predictive capability of the model. Sensitivity studies indicated that the effect of seasonal bathymetric changes on current velocities may be quite significant. The effect of spatially variable bed roughness on the flow field was found to be less significant. The validation results showed that the model is capable of reproducing water levels and current velocities in the study area in fair agreement with observations. The mean absolute errors between computed and observed water levels at a number of locations covering periods of several months were found to be less than 10 cm (3 %of the mean tidal range) and 20 cm (6 %of the mean tidal range) at high and low water levels, respectively. The mean absolute errors between computed and observed depth-averaged velocities at various cross-sections in the tidal channels were generally found to be less than 0.2 m/s, which represents less than 20% of the tidally-averaged value. The model simulation results indicated a certain tendency towards underestimation of current velocities in the tidal channels. On the basis of the quality standards usually adopted (WALSTRA et al., 2001 and VAN RIJN et al., 2002), the performance of the model with regard to current velocity predictions was found to range between good and excellent.

Three-Dimensional Tidal Flow in an Elongated, Rotating Basin

Journal of Physical Oceanography, 2007

The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a linear, constant-density model on the f plane. Rotation fundamentally alters the lateral flow, introducing a lateral recirculation comparable in magnitude to the axial flow, as long as friction is not too large. This circulation is due to the imbalance between the cross-channel sea level gradient, which is in near-geostrophic balance with the Coriolis acceleration associated with the vertically averaged axial flow, and the Coriolis acceleration associated with the vertically sheared axial flow. During flood condition, for example, the lateral Coriolis acceleration near the surface exceeds the pressure gradient, tending to accelerate the lateral flow, while the converse is true near the bottom. As a result, with rotation, fluid parcels tend to corkscrew into and out of the basin in a tidal period. The axial flow is only weakly modified by rotation. When friction is small, the axial velocity is uniform in each section, except in a narrow bottom boundary layer where it decreases to zero. The boundary layer thickness increases with friction, so that with moderate or large friction, axial velocities are sheared from bottom to surface. When friction is large, the local and Coriolis accelerations are both small and the dynamics are governed by a balance between friction and the pressure gradient.

Layer integrated modeling of three dimensional recirculating flows in model tidal basins

Abstract Details are given of a numerical model study to refine a layer integrated model, applied to scaled hydraulic model rectangular tidal basins with large aspect ratios (i.e., L/B = 1/4–4/1), and using two- and zero-equation turbulence models. For the zero-equation turbulence model the mixing length model was deployed to calculate the horizontal eddy viscosity coefficient, whereas for the two-equation model, the depth integrated k-ε turbulence model was used. Likewise, the layer integrated mixing length and k-ε turbulence models were used to determine the vertical eddy viscosity coefficient. The model was first applied to idealized channel flows, with the agreement between the predicted values and experimental data being satisfactory. The model was then tested by applying it to an idealized set of data for wind driven currents in a closed rectangular basin, with good agreement again being obtained between the numerical model results and published experimental data. The model was finally applied to a set of hydraulic model studies, undertaken by the writers for a number of different model rectangular tidal basin configurations (or aspect ratios), each with an asymmetric entrance, a flat bed, and vertical sidewalls. The numerical model results obtained using the k-ε and mixing length turbulence models in the horizontal plane were compared graphically with the experimental results to indicate the best model setup for these model basin configurations. Model simulations were also undertaken to investigate the sensitivity of the eddy circulation structure to the closed boundary representation, within the finite difference scheme, and three different boundary conditions were considered including: the no-slip, semislip, and partial-slip representations. The numerical model results showed that the horizontal current structure obtained using the k-ε model was similar to the results obtained using the mixing length turbulence model. The velocity distributions for the different layers were similar, except near the bed, and the horizontal velocity distribution only showed small variations through much of the water column. The three different representations of the closed boundary condition gave very different tidal circulation patterns within the basins, showing that the representation of the closed boundary was crucial for modeling vorticity in such basins. The model results for the k-ε and mixing length turbulence models were found to be in closest agreement with the experimental results when the no-slip and partial-slip conditions were used, respectively.

Tidal flow simulation in the English Channel and Southern North Sea

Advances in Water Resources, 1989

This paper presents the results of the II Tidal Flow Forum experiment of the English Channel and the southern North Sea. The model applies the FADI (falsified alternating direction implicit) scheme and uses the data base of the Tidal Flow Forum. Discrepancies between the model results and the distributed field data of 11 tide stations and 8 tidal current measurement points are shown graphically and are quantified by calculating the RMS (root mean square) errors and the standard deviations. Sensitivity tests have been carried out by changing some parameters (frictions, Coriolis .... ). The results which best fit the reference data were obtained by using the Manning's friction law. By doing so, the model can more appropriately adapt the complex bathymetry. The improvements are shown graphically.

Depth‐Averaged 2‐D Model of Tidal Flow in Estuaries

2004

A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established using the finite volume method on non-staggered, curvilinear grid. The 2-D shallow water equations are solved by the SIMPLEC algorithm with the Rhie and Chow's momentum interpolation technique. The convection terms are discretized by one of the hybrid upwind/central difference scheme, exponential difference scheme, QUICK scheme and HLPA scheme. The algebraic equations are solved using the strongly implicit procedure (SIP). The model is capable of handling the drying and wetting problem due to the variation of water surface elevation. The model has been tested in Tokyo Bay and San Francisco Bay. The tests show that the present model is very stable and efficient. The simulated water elevation and flow velocity are in good agreement with the measured data.

Basic flow field in a tidal basin

Geophysical Research Letters, 2002

1] A simplified model for tidal flow in a basin is presented. The model is based on the assumption of a flat water surface oscillating synchronously in the tidal basin. Under this hypothesis the depth-averaged continuity equation becomes a Poisson equation that can be easily resolved at each instant of the tidal cycle. This formulation, which is particularly valid for small, deep basins, provides a simplified solution of the depth-integrated shallow water equations and suggests a possible approach to model long-term morphodynamic evolution of tidal basins. The model is tested in San Diego Bay, California, and the results are briefly discussed.

Modeling of channel patterns in short tidal basins

Journal of Geophysical Research, 2005

1] We model branching channel patterns in short tidal basins with two methods. A theoretical stability analysis leads to a relationship between the number of channels and physical parameters of the tidal system. The analysis reveals that width and spacing of the channels should decrease as the slope of the bottom profile and the Shields parameter increase and as the mean water depth decreases. In general, the channel depth should halve at every bifurcation. These theoretical results agree well with the field data from the Dutch Wadden Sea. A numerical model based on Delft3D, a software system of WL/Delft Hydraulics, is used to simulate the time evolution of a channel network in a geometrically simplified basin of similar dimensions as the Wadden Sea basins. The resulting channel network displays a three-times branching behavior, similar to the three-to four-times branching patterns observed in the Wadden Sea. The simulated channel pattern satisfies the relation derived from the theoretical analysis. The results of this pattern analysis provide for additional validation of two-dimensional/three-dimensional process-based morphodynamic models of tidal basins.