Response Times of Salinity in Relation to Changes in Freshwater Inflows in the Lower Hillsborough River, Florida

Xin-jian, Chen; Flannery, Michael S.; Moore, David L.

doi:10.2307/1352899

Cited by 38 publications

(28 citation statements)

References 7 publications

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“…A semi-implicit ÿnite di erence scheme based the FSC method has been developed and implemented in an existing laterally averaged model called LAMFE [1,2,6]. Because the FSC method for the laterally averaged ows is unconditionally stable with respect to the gravity waves, the vertical eddy viscosity term, and the bottom and side wall shear stresses, the semiimplicit scheme based on this method is very e cient and allows a large time step to be used in model runs.…”

Section: Discussionmentioning

confidence: 99%

“…There is also no need to calculate the intermediate vertical velocities (w n+ * i; k ), because they have no role in the calculations in the second step. The implementation of the two steps is straightforward and has been done in a laterally averaged model for estuaries (LAMFE) previously developed by the author [1,2,6]. The ÿrst fractional step of the FSC method includes the following substeps:…”

Section: Implementation Of the Schemementioning

confidence: 99%

“…Flows and water quality parameters vary in the vertical and the longitudinal directions but are relatively homogeneous in the lateral direction. Under the hydrostatic pressure assumption, the laterally averaged continuity, momentum, and transport equations in narrow rivers and estuaries are [1,2] …”

Section: Introductionmentioning

confidence: 99%

“…The ÿrst term on the right side of Equation (5) is the barotropic pressure component, while the second term is the baroclinic pressure component. Inserting Equation (5) into Equation (2) and using the Bousinnesq approximation, one obtains …”

Section: Introductionmentioning

confidence: 99%

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An efficient finite difference scheme for free‐surface flows in narrow rivers and estuaries

Chen

2003

Numerical Methods in Fluids

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SUMMARYThis paper presents a free-surface correction (FSC) method for solving laterally averaged, 2-D momentum and continuity equations. The FSC method is a predictor-corrector scheme, in which an intermediate free surface elevation is ÿrst calculated from the vertically integrated continuity equation after an intermediate, longitudinal velocity distribution is determined from the momentum equation. In the ÿnite di erence equation for the intermediate velocity, the vertical eddy viscosity term and the bottom-and sidewall friction terms are discretized implicitly, while the pressure gradient term, convection terms, and the horizontal eddy viscosity term are discretized explicitly. The intermediate free surface elevation is then adjusted by solving a FSC equation before the intermediate velocity ÿeld is corrected. The ÿnite di erence scheme is simple and can be easily implemented in existing laterally averaged 2-D models. It is unconditionally stable with respect to gravitational waves, shear stresses on the bottom and side walls, and the vertical eddy viscosity term. It has been tested and validated with analytical solutions and ÿeld data measured in a narrow, riverine estuary in southwest Florida. Model simulations show that this numerical scheme is very e cient and normally can be run with a Courant number larger than 10. It can be used for rivers where the upstream bed elevation is higher than the downstream water surface elevation without any problem.

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Section: Discussionmentioning

confidence: 99%

Section: Implementation Of the Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An efficient finite difference scheme for free‐surface flows in narrow rivers and estuaries

Chen

2003

Numerical Methods in Fluids

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“…Model variables are placed at the same level for the same layer. Traditional z-level models use a relatively thick surface layer to cover the variation of the free surface [5], while recent z-level models allow the free surface to travel from one layer to another [6][7][8][9][10]. Depending on the water depth, the number of grid points in the vertical direction varies in a z-level model.…”

Section: Introductionmentioning

confidence: 99%

Using a piecewise linear bottom to fit the bed variation in a laterally averaged, z‐co‐ordinate hydrodynamic model

Chen

2004

Numerical Methods in Fluids

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SUMMARYIn developing a 3D or laterally averaged 2D model for free-surface ows using the ÿnite di erence method, the water depth is generally discretized either with the z-co-ordinate (z-levels) or a transformed co-ordinate (e.g. the so-called -co-ordinate or -levels). In a z-level model, the water depth is discretized without any transformation, while in a -level model, the water depth is discretized after a so-called -transformation that converts the water column to a unit, so that the free surface will be 0 (or 1) and the bottom will be −1 (or 0) in the stretched co-ordinate system. Both discretization methods have their own advantages and drawbacks. It is generally not conclusive that one discretization method always works better than the other. The biggest problem for the z-level model normally stems from the fact that it cannot ÿt the topography properly, while a -level model does not have this kind of a topography-ÿtting problem.To solve the topography-ÿtting problem in a laterally averaged, 2D model using z-levels, a piecewise linear bottom is proposed in this paper. Since the resulting computational cells are not necessarily rectangular looking at the x-z plane, ux-based ÿnite di erence equations are used in the model to solve the governing equations. In addition to the piecewise linear bottom, the model can also be run with full cells or partial cells (both full cell and partial cell options yield a staircase bottom that does not ÿt the real bottom topography). Two frictionless wave cases were chosen to evaluate the responses of the model to di erent treatments of the topography. One wave case is a boundary value problem, while the other is an initial value problem. To verify that the piecewise linear bottom does not cause increased di usions for areas with steep bottom slopes, a barotropic case in a symmetric triangular basin was tested. The model was also applied to a real estuary using various topography treatments. The model results demonstrate that ÿtting the topography is important for the initial value problem. For the boundary value problem, topography-ÿtting may not be very critical if the vertical spacing is appropriate.

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The effect of hydrographs shape on river deltas salinization

Matsoukis

Amoudry

Bricheno

et al. 2021

Preprint

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Response Times of Salinity in Relation to Changes in Freshwater Inflows in the Lower Hillsborough River, Florida

Cited by 38 publications

References 7 publications

An efficient finite difference scheme for free‐surface flows in narrow rivers and estuaries

An efficient finite difference scheme for free‐surface flows in narrow rivers and estuaries

Using a piecewise linear bottom to fit the bed variation in a laterally averaged, z‐co‐ordinate hydrodynamic model

The effect of hydrographs shape on river deltas salinization

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