River Section

Technical details about the river section unit are given below.

The River Section models the flow of water in natural and man-made open channels based on the one-dimensional shallow water or Saint-Venant equations, which express the conservation of mass and momentum of the water body.

Pseudo two dimensional modelling of floodplain flow is also possible with the River unit when different conveyances are calculated for different areas of the channel cross section. Static floodplain storage and sinuosity can also be incorporated. Localised regions of supercritical flow can be modelled approximately.

River section units should not be directly connected to Conduit units. Users can connect CONDUIT and RIVER reaches using a Junction if no head loss occurs at the join. Alternatively the specialised Culvert Inlet and Culvert Outlet units can be used to model the losses associated with transitions from open channel to culverts and vice versa. Bernoulli Loss units are also available to model more generalised losses.

General guidance on river sections

Each Manning's n value applies to the channel between the point defined by the pair of coordinates with which it appears, and the point defined in the next line of data (the last value of Manning's `n' is thus ignored, but still needs to be given).

If a compound channel is being modelled, it is more accurate to subdivide the channel into a number of vertical panels that reflect the geometry of the channel. The conveyance of each of these panels will then be calculated individually (as opposed to calculating the conveyance across the full width of the channel as a whole) and then summed across the channel. If this approach is required, append a panel marker on the line corresponding to the first coordinates of the panel. The panel limits are from the * panel marker to data line before the next * marker.

Due to the way Flood Modeller calculates panel properties, it is important to realise that narrow panels will not contribute significantly to the section conveyance. This is because the property calculations are based around flow areas for various water levels. The flow area for a panel that is close to vertical will be very small for all water level values.  Users will be warned if panels are so narrow that they are unlikely to contribute very much to the total cross-section conveyance.

The user is warned if Manning's 'n' varies by more than 20% in any panel. Manning's 'n' values should not vary substantially within panels.

For compound channels, consisting of a meandering low flow channel in a much straighter flood plain, the ratio of the flow path length in the flood plain to the flow path length in the low flow channel can be included after each panel `*' marker. The declared relative path length ratio will then apply to the coordinates on the subsequent data sets until the next panel marker `*' is encountered. Each change in path length ratio must be declared with an accompanying `*' panel marker. The relative path length ratio has a default value of 1.0 and cannot be negative.

It is possible to specify left and right deactivation markers, which specify areas of the cross-section which will not be processed as section data. This enables a full section to be input, even if only the in-bank portion, say, is to be used for computational purposes. This allows quicker switching between models used for 2d-coupling or quasi-2d modelling using off-line cells or parallel channels and those using extended cross-sections, without the need to remove or reinstate the extraneous data.

If `dead' flood plain storage (i.e. no conveyance) is to be used a Manning's `n' value of zero should be entered for the relevant panels. A first order modelling of flood plain flow is also incorporated, by modifying the storage width and conveyance terms. This is activated by entering non-zero values of `n' over the flood plain areas.

Supercritical flow can be accommodated in localised regions by simplifying the momentum equation by treatment of part of the convective acceleration term:

The Parameters section of the run form contains the Lower Froude limit below which no simplification is carried out and the Upper Froude limit above which the simplified equation is used. If the computed Froude number is between the lower and upper limits a weighted average is taken between the two approaches. Recommended (default) values for the limits are 0.75 for the lower limit and 0.9 for the upper limit.

The simplified equation will only be used at nodes where the Froude number is above the lower limit - the rest of the network will be solved using the full Saint-Venant equations.

Using Levees 

Levees can be added as special markers to your river sections. The effect of this is best visualised.

Adding levees to your model will also add the levee floodplain data as an additional output. This creates four variables (which can subsequently be displayed as time series results, etc.), namely:

• Left FP h – the water elevation (in m or ft) in the left floodplain (i.e. beyond the left levée marker)
• Right FP h – the water elevation (in m or ft) in the right floodplain (i.e. beyond the right levée marker)
• Left FP mode – the status of the left floodplain (see below)
• Right FP mode – the status of the right floodplain (see below)

The floodplain modes are denoted as follows:

1. Floodplain dry – water level has not exceeded levée, or has completely drained
2. Transition – water level has overtopped the levée, but has not yet reached full/transition depth
3. Full – water level exceeds transition depth; floodplain level is equal to main channel level
4. Recession – water level has receded below levée level after becoming overtopped; recedes at the same rate as the main channel :

Add levees to your river sections using the 'Special Marker' option within individual river section nodes:

Levees can be added to multiple river sections using the 'Change River Section Markers' tool in the toolbox. For example, deactivation markers in multiple river sections can be adjusted to levee markers using the tool.

Using the 'Change River Section Markers' tool:

Note that when adding Levée markers based on (existing) panel markers, exactly two panel markers must be present per section (otherwise, the tool will add no markers for that particular section). This is so that it can determine unambiguously which is the left and right marker. When you have used the tool, you will be notified of the number of river sections that have changed (and therefore can determine if any have not changed).

When using levees, a weir-like effect will be produced as the water level exceeds the height of the levee marker and the flow transitions between the (single) main channel flow to a flow across both the main channel and side channel(s). The 'Levee Transition Depth' indicates the length of this transition.

The levee transition depth (default=1m) can be adjusted in the 1D advanced parameters; however it should be noted that too small a transition will lead to a relatively rapid increase in wetted area (and hence channel volume) from in-bank to full floodplain, and should therefore be avoided.

How to adjust the levee transition depth in the advanced parameters:

Data required for river sections

Equations used for river sections

The equations used by a River Section are the mass conservation or continuity equation:

and the momentum conservation or dynamic equation: 

The assumptions made in order to derive this form of the equations are:

1. The flow is one dimensional - a single velocity and elevation can be used to describe the state of the water body in a cross-section.
2. The streamline curvature is small and vertical accelerations negligible; hence the pressure is hydrostatic.
3. The effects of boundary friction and turbulence can be accounted for by representations of channel conveyance derived for steady state flow.
4. The average channel bed slope is small enough such that the small angle approximation can be used.
5. All the functions and variables are continuous and differentiable (which precludes the proper modelling of bores or hydraulic jumps).

Spatially-varying density

In river systems when the density varies significantly along its length, e.g. in tidal rivers, where salinity affects the density longitudinally, the spatially-varying density can have a significant effect on the water levels. Thus a representative density value may be [optionally] specified for each river node.

Notes:

If no density term is entered, the density defaults to 1000 kg/m³. Therefore it is important to specify the density for every node, where density is significant, if using this facility

If the density does not vary spatially, then the density terms cancel out of the momentum equation.

The method used to represent spatially-varying density is a simplification and if used may lead to errors in the mass balance reporting.

Conveyance

Conveyance is calculated at a given water level by splitting the cross section into a set of user defined vertical panels and summing the contribution from each panel. The advantages of this approach over the case where no panels are employed is that the conveyance does not decrease as the water begins to exceed the bank full level. In the simple case without panels, the wetted perimeter increases significantly over a short range of water levels, without a corresponding large increase in area, which leads to an unphysical reduction in conveyance.

A panel marker indicates a new panel whose first point is the offset on the same line.

The formula used to calculate conveyance, K, at a given stage, h, is as follows:

Example

In the above diagram, the conveyance at water level h₁ has a contribution from panel B only, whereas panels A, C and D would contribute to the conveyance for water level h₂. If it is not required that panel D should contribute to the conveyance at water levels below y_k, then the point (x_n, y_n) should not be included in the channel data. In the case where a natural or man-made levee is included in the cross section data, anomalous results may be observed at water levels around the highest point. In cases where the embankment height is significant, it is more accurate to use a Spill and a Reservoir (or another channel if channel momentum is significant). In this case, the maximum embankment heights along the channel should be included in the spill and any cross sections data further away from the channel than the maximum height should be removed. In effect, it is always assumed that there is a flow path to all points in the section lower than any local maximum.

To illustrate the conveyance calculation, for water level h_i, the conveyance is given by:

The very simple example below for a triangular cross section with a 45° side slope further demonstrates how the formula is applied.

With n = 0.03 and rpl = 1

At a water level, y = 0.5m:

Flood Modeller calculates conveyance at a set of water levels, including all of those in the cross section data, and then performs a linear interpolation to obtain conveyance at any intermediate water levels. A consequence is that you should not specify a very small number of points to represent a deep cross section as this can lead to inaccuracies in the representation of the nonlinear conveyance function, particularly at small depths.

Flood Modeller will add extra points where it deems necessary but even these may not be sufficient for very deep sections with few user defined points and it is recommended that extra points are added in this case, particularly near water levels of main interest. It is also advantageous to specify a unique thalweg in this situation.

Relative path length

Relative path length is a measure of the sinuosity associated with each of the vertical panels, relative to the sinuosity of the main channel. Since it is a property of a particular cross section, it should be calculated from the mid point of the distance from the previous section to the mid point of the distance to the subsequent section as illustrated below, where x is the approximate distance to the centroid of the panel.

Illustration of the effects of sinuosity on path length:

Parameters used to calculate path length:

For the above case we have for Section B:

Datafile format

Line 1 - keyword `RIVER' [comment]

Line 2 - keyword `SECTION'

Line 3 - Label1[, Label2, Label3][, Label4, Label5, Label6, Label7]

Line 4 - dx

Line 5 - n₁

Line 6 to Line 5+n₁ - x_i, y_i, n_i[, *, r_i LRB, easting, northing, deactivate_marker]

Notes

• The format of lines 6 to 5+n1 is in keeping with the general width of ten characters per field, although the panel marker '*' and relative path length r_i are lumped together in one field, the first character of which must either be blank (no panel marker) or '*' (panel marker present). In FORTRAN parlance, the format is F10.0, F10.0, F10.0, A1, F9.0, A10, F10.0, F10.0.
• Although the easting and northing coordinates are not read by the simulation, except when using the wind shear unit, the coordinates can be exported (for subsequent importation into GIS tools, for example) by using the option in the TabularCSV tool.

Example