Contributed by Rory O'Hara Murray from Marine Scotland

The tidal turbine ‘module’ for FVCOM is a simple momentum sink following the approach of Yang et al. (2013) and is described in O'Hara Murray and Gallego (2016). Only the momentum sink contribution due to the thrust exhibited on the flow by the turbine is included. Yang et al. also included additional drag terms (due to support structures and blades) which could easily be added to the code.

Additional features included in the current FVCOM tidal turbine module are:

• The ability to specify which sigma layers to put the momentum sink in, i.e. the fractional spit between the sigma layers. For example in a 50 m deep model element with 10 sigma layers a 20 m tidal turbine might only occupy sigma layers 6 – 9. This could be split with a fraction of 1/4 in each of the four sigma layers, or with 1/5, 1/3, 1/3 and 1/5 in layers 6 - 9, respectively, for example. There is a Matlab function in the FVCOM toolbox to calculate the fractional split between sigma layers for a circular rotor swept area.
• A speed depended thrust coefficient using the thrust coefficient defined in the TeraWatt project (TeraWatt 2015). This is updated every time step.

The module works by adding additional terms to the momentum equations in the internal and external modes. This is done for all model elements and those model elements which have no momentum sink, i.e. no turbines, have a momentum sink contribution of zero. The zero contribution in elements with no turbines in is ensured by setting the number of turbines in those elements (NTT) to zero.

&NML_NETCDF
 NC_CT = F	! T/F
 NC_KBTT = F	! T/F
&NML_PHYSICS
 TIDAL_TURBINE_ON = T                       ! T/F turn tidal turbine module on/off
 TIDAL_TURBINE_FILE = 'Tidal_Turbines.nc'   ! tidal turbine input file
 TIDAL_TURBINE_KIND = 'momentum_sink'       ! momentum_sink or bottom_roughness
 TIDAL_TURBINE_CT   = 'constant'            ! constant or variable (to use the TeraWatt speed dependent CT curve)

The NC_CT and NC_KBTT flags are for outputting the arrays containing the tidal turbine thrust coefficient, CT, and the fractional split between sigma layers, KBTT, respectively, to the netCDF output file. This is for checking primarily and is not necessarily recommended for normal usage (i.e. set to F).

• KBTT: array specifying the fraction of each sigma layer that the turbines are located in, for each model element.
• CT: array specifying the thrust coefficient of the turbine(s) in each model element (zero everywhere by default). Updated every time step (speed dependent).
• AREATT: array specifying the rotor swept area of the turbine(s) in each model element.
• NTT: array specifying the number of turbines in each model element.

Note that KBTT, AREATT and NTT should be set to zero everywhere (equating to no momentum deduction) apart from those elements with tidal turbines in. These are defined in the tidal turbine netcdf input file. The variables in the netcdf input file are listed below, and NTT = turbine_number; KBTT = turbine_sigma_layer; AREATT = swept_area.

• Dimensions: nele, siglay (number of model grid elements and sigma layers)
• Variables:
• turbine_number (nele): Number of turbines in each element
• turbine_sigma_layer (siglay, nele): The fraction of each sigma layer that the turbines are located in
• swept_area (nele): Area (m² ) swept by turbine rotor blades
• thrust (nele): The thrust constant coefficient. Note that this is used when the Ct values are constant, otherwise the hard coded speed variable Ct values are used.

• write_FVCOM_TT.m - create the netCDF input file
• turbine_area_sigma.m - calculate the turbine fractional split between sigma layers
• tidal_turbine_example.m - an example script for creating a tidal turbine input file (using the above functions)

O’Hara Murray, R., A. Gallego (2017) A modelling study of the tidal stream resource of the Pentland Firth, Scotland. Renewable Energy 102, 326-340. doi:10.1016/j.renene.2016.10.053

TeraWatt (2015) TeraWatt Position Papers http://www.masts.ac.uk/media/166596/position_papers_terawatt_e-book.pdf ISBN: 978-0-9934256-0-8

Yang, Z., T. Wang and E. Copping (2013) Modelling tidal stream energy extraction and its effects on transport processes in a tidal channel and bay system using a three-dimensional coastal ocean model, Renewable Energy 50, 605-613. doi:10.1016/j.renene.2012.07.024