Wind Shear

The Wind Unit models the effects of wind shear on open-channel sections, which may be of particular significance in wide rivers and estuaries.

Theory and Guidance

The ability to model the effects of wind shear on open-channel sections, which may be of particular significance in wide rivers and estuaries, is now available within Flood Modeller.

The St Venant momentum equation used in Flood Modeller may now include a term allowing for a wind shear stress component. The wind shear stress term (e.g. Falconer and Chen ) of , having neglected the transverse component (perpendicular to flow direction), is added to the St Venant momentum equation to give

Evaluation of wind shear term

Many proposals exist for the magnitude wind shear stress, but the following from Gill is widely accepted:

The drag coefficient may vary with velocity in practice, although it will remain as a modifiable constant value in Flood Modeller (default = 0.0011). Similarly, the water and air densities will be modifiable by the user (defaulting to 1000 and 1.2 kg m^-3 respectively).

Since this is being applied to a 1-d model, the transverse component of the stress term will be ignored. To determine the component of the wind shear in the direction of flow, the angle between the wind and river orientation is required to be calculated.

The river data (width and orientation) may be obtained from River Section data. The latter will default to being obtained from easting/northing coordinates the data file, but may be obtained from other sources, such as the schematic files (*.gxy) or a comma-separated variable (*.csv) file, with format easting, northing, node_label, unit type [optional].

The St Venant equations can therefore be rewritten, accounting for wind shear, as:

Notes

1. Wind data for use within Flood Modeller may be specified within an event file (e.g. .ied) and/or data file (.dat). Only one Wind data unit is allowed (any subsequent occurrences will be ignored), although one can apply more than one wind time series (relating to different locations) in the same unit.
2. The node label of the Wind unit is for reference purposes only and has no effect on the node count or connectivity of the model
3. Wind data may be applied globally to the model at any one time, or different wind data sets maybe applied to different groups of nodes. Each set of wind data may have a list of river nodes associated with it and will apply the wind shear effects to that list of nodes.
4. By default, all open channel sections (including replicated and interpolated sections, unless applied to conduits) will have the wind shear applied to them from the default wind data set. This may be overridden by referencing the channel section in the non-default wind data set. Closed conduits will not have wind effects applied to them.
5. Any extra data relating to the river sections (e.g. direction of river centreline) may be obtained from the main data file or elsewhere. Currently existing sources of calculating the river centreline bearing are the Eastings/Northings fields in the data file, the schematic file (*.gxy), or a simple csv file of the format easting, northing, node_label .
6. Wind speed and bearing will be interpolated at model times between those specified in the input data. When interpolating the wind bearing, the bearing will remain in the range [0°, 360°) and will interpolate using the shortest path, for instance interpolating between 10° and 350° will give a result in the range [0°, 10°] or [350°, 360°).

Datafile Format

Wind unit

Line 1 - Header 'WIND DATA',

Line 2 - Revision number, [comment]

Line 3 - windmeth, centreline

Line 4 - external source file name (absolute or relative; leave blank if centreline='DATFILE')

Line 5 - r_w, r_air, c_d.

Line 6 - nwinds

The following block is repeated nwinds times:

Line 7.1 - windnod, [comment]

Line 7.2 - n₁, [tlag], [t_m], [repeat], [smooth], [wsmult], [bearing_type], [globflag]

Line 7.3.1 to Line (7.3.n1) - ws_i, θ_i, t_i, [d_i]

Line 7.4 - 'NODES'

Line 7.5 - nodecount

Line 7.5.1 to Line (7.5.nodecount) - node1, [node2]

where:

windmeth = 'GLOBAL' or 'LOCAL' depending on whether wind is applied globally or locally. GLOBAL applies the wind data set denoted by globflag='DEFAULT' (the first occurrence thereof - with warning - if multiple, or first data set if absent) to all river units (unless overridden by a different wind unit identifier)

centreline = keyword 'DATFILE' or 'GXYFILE' to denote from where the river direction information is obtained

ρ_w = density of water (kg m^-3; default 1000).

ρ_air = density of air (kg m^-3; default 1.2).

c_d = drag coefficient (dimensionless, default 0.0011).

nwinds = number of sets [e.g. gauge sites] of wind data

windnod = wind data set (dummy) node identifier

globflag = 'DEFAULT' for default global wind set; blank otherwise

n₁ = Number of ensuing flow and time data sets

t_lag = Optional time-datum adjustment. This value can be used to reduce all time values by the given value. For example, if the Time-Datum adjustment is set to 2.2 and the units of time are hours then all time values will be reduced by 2.2 hours (the windspeed profile is moved 2.2 hours earlier). Default value is 0.

t_m = optional keyword or value for units of time in the following data set. Can be any numerical multiplier or one of the following: seconds (the default), minutes, hours, days, weeks, fortnight, lunar (month), months (of 30 days), quarter, years, decades or dates.

repeat = policy for extending data if the run finishes after the end of the boundary data.

Options are:

REPEAT - if the data are to be repeated from the beginning

EXTEND - if the flow is to be fixed at the last given value

NOEXTEND - for no extension

If NOEXTEND is used then the program will stop with an error message if there are insufficient boundary data.

smooth = SPLINE if a cubic spline is to be fitted to the data, or LINEAR to use linear interpolation. (If the field is blank then linear interpolation is used.)

wsmult = Windspeed multiplier or keyword. Numeric - user input multiplier for windspeed. Particularly useful in converting non-standard units to m/s, e.g. if the data is entered as miles per hour, then setting this value to 0.45 will convert the values in the windspeed table to m/s. Recognised keywords are "m/s", "mph", "kph" or "km/h" and "knots". The recognised keywords will replace the multiplier. The default multiplier is 1 (which will occur in the case of an invalid keyword).

Bearing_type = 'TO'(default) - direction towards which wind is blowing; 'FROM' - direction from which wind is blowing.

ws_i = Windspeed corresponding to t_i (defaults to m/s, but see wsmult)

θ_i = bearing of wind at time t_i.

t_i = time (in units of t_m - default of seconds). If t_m is set to 'DATES', then this must be a time of day in 24-hour dd:mm format (e.g. 20:45).

d_i = date (only used if t_m is set to 'DATES') in dd/mm/yyyy format.

nodecount = number of subsequent lines of nodes/node pairs

node1 = wind data from this station will override the default station for all open channel units downstream of node1, until it encounters a dx=0, or ...

...node2 = wind data from this station will override the default station for all open channel units downstream of node1 and upstream of node2.

Data file example

NB the first line [123456...] displayed is not part of the file, but is shown to demonstrate column widths: