Depth‐Averaged 2‐D Model of Tidal Flow in Estuaries (original) (raw)
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Improved numerical modelling of estuarine flows
Abstract Three key improvements to a widely used numerical model for predicting depth-averaged shallow water flows in estuarine and coastal waters are outlined herein. They include the adoption of a new grid layout for calculating friction and viscosity, a new method for simulating flooding and drying processes and a better representation of irregular wall boundaries. Although these improvements are currently implemented in the Depth Integrated Velocities And Solute Transport (DIVAST) model, they can easily be extended to other numerical models in the framework of a finite-difference or finite-volume method on a space-staggered rectangular grid system. Much effort has been made to keep the improvements simple and efficient so that they can be used in long-term and large-area simulations of estuarine and coastal flows. Numerical tests have been undertaken to verify the performance of these refinements for idealised bed forms, different beach configurations and irregular shoreline boundaries. The results show that for all conditions these refinements produce either the same or better results than the original model. Finally, the refined numerical model was used to simulate the tidal flow in a natural coastal basin. On the whole, the predicted variations in the inundation areas and the velocity fields were reproduced more accurately for different stages of the tide. At field measurement sites, the predicted water levels and velocities agreed favourably with the measured data.
Ocean Engineering, 2008
A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous
Numerical model for the study of hydrodynamics on bays and estuaries
Applied Mathematical Modelling, 1992
A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow wa ter equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric. Lagrangian elements. To obtain the different element matrices , Simpson numerical integration has been applied. For time integration of the model. several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step t.t; however, central differences time inteKration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally. an application to the Bay of Santander is also presented.
Modelling estuarine and coastal flows using an unstructured triangular finite volume algorithm
Abstract Details are given of the development and application of a numerical model for predicting free-surface flows in estuarine and coastal basins using the finite volume method. Both second- and third-order accurate and oscillation free explicit numerical schemes have been used to solve the shallow water equations. The model deploys an unstructured triangular mesh and incorporates two types of mesh layouts, namely the ‘cell centred’ and ‘mesh vertex’ layouts, and provides a powerful mesh generator in which a user can adjust the mesh-size distribution interactively to create a desirable mesh. The quality of mesh has been shown to have a major impact on the overall performance of the numerical model. The model has been applied to simulate two-dimensional dam break flows for which transient water level distributions measured within a laboratory flume were available. In total 12 model runs were undertaken to test the model for various flow conditions. These conditions include: (1) different bed slopes (ranging from zero to 0.8%), (2) different upstream and downstream water level conditions, and (3) initially wet and dry bed conditions, downstream of the dam. Detailed comparisons have been made between model predicted and measured water levels and good agreement achieved between both sets of results. The model was then used to predict water level and velocity distributions in a real estuary, i.e. the Ribble Estuary, where the bed level varies rapidly at certain locations. In order to model the whole estuary, a 1-D numerical model has also been used to model the upper part of the estuary and this model was linked dynamically to the 2-D model. Findings from this application are given in detail.
Journal of Geophysical Research, 2007
An unstructured grid, finite volume, three-dimensional (3-D) primitive equation coastal ocean model (FVCOM) has been developed for the study of coastal ocean and estuarine circulation by Chen et al. (2003a). The finite volume method used in this model combines the advantage of finite element methods for geometric flexibility and finite difference methods for simple discrete computation. Currents, temperature, and salinity are computed using an integral form of the equations, which provides a better representation of the conservative laws for mass, momentum, and heat. Detailed comparisons are presented here of FVCOM simulations with analytical solutions and numerical simulations made with two popular finite difference models (the Princeton Ocean Model and Estuarine and Coastal Ocean Model (ECOM-si)) for the following idealized cases: wind-induced long-surface gravity waves in a circular lake, tidal resonance in rectangular and sector channels, freshwater discharge onto the continental shelf with curved and straight coastlines, and the thermal bottom boundary layer over the slope with steep bottom topography. With a better fit to the curvature of the coastline using unstructured nonoverlapping triangle grid cells, FVCOM provides improved numerical accuracy and correctly captures the physics of tide-, wind-, and buoyancy-induced waves and flows in the coastal ocean. This model is suitable for applications to estuaries, continental shelves, and regional basins that feature complex coastlines and bathymetry.
International Journal for Numerical Methods in Fluids, 2000
A three-dimensional baroclinic numerical model has been developed to compute water levels and water particle velocity distributions in coastal waters. The numerical model consists of hydrodynamic, transport and turbulence model components. In the hydrodynamic model component, the Navier -Stokes equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. The transport model component consists of the pollutant transport model and the water temperature and salinity transport models. In this component, the three-dimensional convective diffusion equations are solved for each of the three quantities. In the turbulence model, a two-equation k-formulation is solved to calculate the kinetic energy of the turbulence and its rate of dissipation, which provides the variable vertical turbulent eddy viscosity. Horizontal eddy viscosities can be simulated by the Smagorinsky algebraic sub grid scale turbulence model. The solution method is a composite finite difference -finite element method. In the horizontal plane, finite difference approximations, and in the vertical plane, finite element shape functions are used. The governing equations are solved implicitly in the Cartesian co-ordinate system. The horizontal mesh sizes can be variable. To increase the vertical resolution, grid clustering can be applied. In the treatment of coastal land boundaries, the flooding and drying processes can be considered. The developed numerical model predictions are compared with the analytical solutions of the steady wind driven circulatory flow in a closed basin and of the uni-nodal standing oscillation. Furthermore, model predictions are verified by the experiments performed on the wind driven turbulent flow of an homogeneous fluid and by the hydraulic model studies conducted on the forced flushing of marinas in enclosed seas.
Analytical description of tidal dynamics in convergent estuaries
Journal of Geophysical Research, 2008
1] Analytical solutions of the one-dimensional hydrodynamic equations for tidal wave propagation are now available and, in this paper, presented in explicit equations. For given topography, friction, and tidal amplitude at the downstream boundary, the velocity amplitude, the wave celerity, the tidal damping, and the phase lag can be computed. The solution is based on the full nonlinearized St. Venant equations applied to an exponentially converging channel, which may have a bottom slope. Two families of solutions exist. The first family consists of mixed tidal waves, which have a phase lag between zero and p/2, which occur in alluvial coastal plain estuaries with almost no bottom slope; the second family consists of ''apparent standing'' waves, which develop in short estuaries with a steep topography. Asymptotic solutions are presented for progressive waves, frictionless waves, waves in channels with constant cross section, and waves in ideal estuaries where there is no damping or amplification. The analytical method is accurate in the downstream, marine part of estuaries and particularly useful in combination with ecological or salt intrusion models. The solutions are compared with observations in the Schelde, Elbe, and Mekong estuaries.
A mathematical model study of the flushing characteristics of a shallow tidal bay
The Paper describes the development and application of a mathematical model to compare the hydraulic features and flushing characteristics of Holes Bay in Dorset, for the present boundary configuration and for two proposed new outlines of the bay. The time dependent non-linear equations of mass, momentum and advective-diffusion were solved numerically using a finite difference scheme, with the effects of the earth's rotation, bed friction, a surface wind stress and a simple turbulence model being included in the momentum equations.
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