.. _FF:Nomenclature:

Nomenclature
============

.. container::
   :name: Tab:FF:Nomenclature

   .. table:: List of Available FAST.Farm Output Channels

      ================= ==================
      |eqs_ABLSolver|   |txt_ABLSolver|
      |eqs_AWAE|        |txt_AWAE|
      |eqs_ar|          |txt_ar|
      |eqs_ak|          |txt_ak|
      |eqs_BEM|         |txt_BEM|
      |eqs_bK|          |txt_bK|
      |eqs_cOWk|        |txt_cOWk|
      |eqs_cmax|        |txt_cmax|
      |eqs_cmeander|    |txt_cmeander|
      |eqs_cnearwake|   |txt_cnearwake|
      |eqs_cWakeDiam|   |txt_cWakeDiam|
      |eqs_cDMaxAmb|    |txt_cDMaxAmb|
      |eqs_CDMaxShr|    |txt_CDMaxShr|
      |eqs_Ctr|         |txt_Ctr|
      |eqs_Cohij|       |txt_Cohij|
      |eqs_DLL|         |txt_DLL|
      |eqs_DWM|         |txt_DWM|
      |eqs_DGrid|       |txt_DGrid|
      |eqs_DRotor|      |txt_DRotor|
      |eqs_DnpWake|     |txt_DnpWake|
      |eqs_FLORIS|      |txt_FLORIS|
      |eqs_f|           |txt_f|
      |eqs_fc|          |txt_fc|
      |eqs_fnbr|        |txt_fnbr|
      |eqs_fmax|        |txt_fmax|
      |eqs_FAmb|        |txt_FAmb|
      |eqs_FShr|        |txt_FShr|
      |eqs_HFM|         |txt_HFM|
      |eqs_HPC|         |txt_HPC|
      |eqs_I|           |txt_I|
      |eqs_K|           |txt_K|
      |eqs_kAmb|        |txt_kAmb|
      |eqs_kShr|        |txt_kShr|
      |eqs_LES|         |txt_LES|
      |eqs_MFoR|        |txt_MFoR|
      |eqs_MPI|         |txt_MPI|
      |eqs_NaN|         |txt_NaN|
      |eqs_NREL|        |txt_NREL|
      |eqs_N|           |txt_N|
      |eqs_Nb|          |txt_Nb|
      |eqs_Nnp|         |txt_Nnp|
      |eqs_NWake|       |txt_NWake|
      |eqs_NP|          |txt_NP|
      |eqs_Nr|          |txt_Nr|
      |eqs_Nt|          |txt_Nt|
      |eqs_OF|          |txt_OF|
      |eqs_OpenMP|      |txt_OpenMP|
      |eqs_pHub|        |txt_pHub|
      |eqs_pPlane|      |txt_pPlane|
      |eqs_RAM|         |txt_RAM|
      |eqs_RSS|         |txt_RSS|
      |eqs_r|           |txt_r|
      |eqs_rPlane|      |txt_rPlane|
      |eqs_SOWFA|       |txt_SOWFA|
      |eqs_t|           |txt_t|
      |eqs_TIAmb|       |txt_TIAmb|
      |eqs_ud|          |txt_ud|
      |eqs_Vadvect|     |txt_Vadvect|
      |eqs_VAmbHigh|    |txt_VAmbHigh|
      |eqs_VAmbLow|     |txt_VAmbLow|
      |eqs_VDistHigh|   |txt_VDistHigh|
      |eqs_VDistLow|    |txt_VDistLow|
      |eqs_VHub|        |txt_VHub|
      |eqs_Vnp|         |txt_Vnp|
      |eqs_Vr|          |txt_Vr|
      |eqs_Vrnp|        |txt_Vrnp|
      |eqs_VTK|         |txt_VTK|
      |eqs_VxRel|       |txt_VxRel|
      |eqs_Vx|          |txt_Vx|
      |eqs_VxnpWake|    |txt_VxnpWake|
      |eqs_DiskAvgVx|   |txt_DiskAvgVx|
      |eqs_wnWind|      |txt_wnWind|
      |eqs_WD|          |txt_WD|
      |eqs_WISDEM|      |txt_WISDEM|
      |eqs_xxnp|        |txt_xxnp|
      |eqs_XYZ|         |txt_XYZ|
      |eqs_hatXYZ|      |txt_hatXYZ|
      |eqs_xd|          |txt_xd|
      |eqs_Xd|          |txt_Xd|
      |eqs_hatxDisk|    |txt_hatxDisk|
      |eqs_hatxnpPlane| |txt_hatxnpPlane|
      |eqs_yd|          |txt_yd|
      |eqs_Yd|          |txt_Yd|
      |eqs_zbot|        |txt_zbot|
      |eqs_alpha|       |txt_alpha|
      |eqs_DeltaT|      |txt_DeltaT|
      |eqs_YawErr|      |txt_YawErr|
      |eqs_nuT|         |txt_nuT|
      |eqs_rho|         |txt_rho|
      |eqs_TwoD|        |txt_TwoD|
      |eqs_ThreeD|      |txt_ThreeD|
      ================= ==================

.. |eqs_ABLSolver|   replace:: ABLSolver
.. |txt_ABLSolver|   replace:: atmospheric boundary layer solver
.. |eqs_AWAE|        replace:: AWAE
.. |txt_AWAE|        replace:: ambient wind and array effects (module)
.. |eqs_ar|          replace:: :math:`a(r)`
.. |txt_ar|          replace:: axial induction factor, distributed radially
.. |eqs_ak|          replace:: :math:`a_K`
.. |txt_ak|          replace:: coherence decrement parameter
.. |eqs_BEM|         replace:: BEM
.. |txt_BEM|         replace:: blade-element momentum
.. |eqs_bK|          replace:: :math:`b_K`
.. |txt_bK|          replace:: coherence offset parameter
.. |eqs_cOWk|        replace:: :math:`C^\text{O}_\text{HWkDfl}`, :math:`C^\text{OY}_\text{HWkDfl}`, :math:`C^\text{x}_\text{HWkDfl}`, and :math:`C^\text{xY}_\text{HWkDfl}`
.. |txt_cOWk|        replace:: calibrated parameters in the horizontal wake-deflection correction
.. |eqs_cmax|        replace:: :math:`c_\text{max}`
.. |txt_cmax|        replace:: maximum blade chord length
.. |eqs_cmeander|    replace:: :math:`C_\text{Meander}`
.. |txt_cmeander|    replace:: calibrated parameter for wake meandering
.. |eqs_cnearwake|   replace:: :math:`C_\text{NearWake}`
.. |txt_cnearwake|   replace:: calibrated parameter in the near-wake correction
.. |eqs_cWakeDiam|   replace:: :math:`C_\text{WakeDiam}`
.. |txt_cWakeDiam|   replace:: calibrated parameter in the wake-diameter  calculation
.. |eqs_cDMaxAmb|    replace:: :math:`C^\text{DMax}_{\nu \text{Amb}}`, :math:`C^\text{DMin}_{\nu \text{Amb}}`, :math:`C^\text{Exp}_{\nu Amb}`, and :math:`C^\text{FMin}_{\nu Amb}`
.. |txt_cDMaxAmb|    replace:: calibrated parameters in the eddy-viscosity filter function for ambient turbulence
.. |eqs_CDMaxShr|    replace:: :math:`C^\text{DMax}_{\nu \text{Shr}}`, :math:`C^\text{DMin}_{\nu \text{Shr}}`, :math:`C^\text{Exp}_{\nu \text{Shr}}`, and :math:`C^\text{FMin}_{\nu \text{Shr}}`
.. |txt_CDMaxShr|    replace:: calibrated parameters in the eddy-viscosity filter function for the wake shear layer
.. |eqs_Ctr|         replace:: :math:`^\text{AzimAvg}C_t(r)` and :math:`^\text{FiltAzimAvg}C_t(r)`
.. |txt_Ctr|         replace:: azimuthally averaged thrust-force coefficient (normal to a rotor disk), distributed radially, and its low-pass time-filtered value
.. |eqs_Cohij|       replace:: :math:`Coh_{i,j}`
.. |txt_Cohij|       replace:: magnitude of partial coherence between points :math:`i` and :math:`j`
.. |eqs_DLL|         replace:: DLL
.. |txt_DLL|         replace:: dynamic-link library
.. |eqs_DWM|         replace:: DWM
.. |txt_DWM|         replace:: dynamic wake meandering
.. |eqs_DGrid|       replace:: :math:`D_\text{Grid}`
.. |txt_DGrid|       replace:: Assumed rotor diameter when generating TurbSim inflow
.. |eqs_DRotor|      replace:: :math:`D^\text{Rotor}` and :math:`^\text{Filt}D_{n_p}^\text{Rotor}`
.. |txt_DRotor|      replace:: rotor diameter and its low-pass time-filtered value at wake plane :math:`n_p`
.. |eqs_DnpWake|     replace:: :math:`D_{n_p}^\text{Wake}`
.. |txt_DnpWake|     replace:: wake diameter at wake plane :math:`n_p`
.. |eqs_FLORIS|      replace:: FLORIS
.. |txt_FLORIS|      replace:: FLOw Redirection and Induction in Steady state
.. |eqs_f|           replace:: :math:`f`
.. |txt_f|           replace:: frequency
.. |eqs_fc|          replace:: :math:`f_c`
.. |txt_fc|          replace:: cutoff (corner) frequency of the low-pass time filter
.. |eqs_fnbr|        replace:: :math:`\vec{f}_{n_b}(r)`
.. |txt_fnbr|        replace:: aerodynamic applied loads distributed radially per unit length for blade :math:`n_b`
.. |eqs_fmax|        replace:: :math:`f_\text{max}`
.. |txt_fmax|        replace:: maximum excitation frequency
.. |eqs_FAmb|        replace:: :math:`F_{\nu \text{Amb}}(x)`
.. |txt_FAmb|        replace:: eddy-viscosity filter function associated with ambient turbulence
.. |eqs_FShr|        replace:: :math:`F_{\nu \text{Shr}}(x)`
.. |txt_FShr|        replace:: eddy-viscosity filter function associated with the wake shear layer
.. |eqs_HFM|         replace:: HFM
.. |txt_HFM|         replace:: high-fidelity modeling
.. |eqs_HPC|         replace:: HPC
.. |txt_HPC|         replace:: high-performance computer
.. |eqs_I|           replace:: :math:`I`
.. |txt_I|           replace:: three-by-three identify matrix
.. |eqs_K|           replace:: :math:`K`
.. |txt_K|           replace:: velocity components :math:`u`, :math:`v`, and :math:`w`
.. |eqs_kAmb|        replace:: :math:`k_{\nu \text{Amb}}`
.. |txt_kAmb|        replace:: calibrated parameter for the influence of ambient turbulence in the eddy viscosity
.. |eqs_kShr|        replace:: :math:`k_{\nu \text{Shr}}`
.. |txt_kShr|        replace:: calibrated parameter for the influence of the wake shear layer in the eddy viscosity
.. |eqs_LES|         replace:: LES
.. |txt_LES|         replace:: large-eddy simulation
.. |eqs_MFoR|        replace:: MFoR
.. |txt_MFoR|        replace:: moving frame of reference
.. |eqs_MPI|         replace:: MPI
.. |txt_MPI|         replace:: message-passing interface
.. |eqs_NaN|         replace:: NaN
.. |txt_NaN|         replace:: not a number
.. |eqs_NREL|        replace:: NREL
.. |txt_NREL|        replace:: National Renewable Energy Laboratory
.. |eqs_N|           replace:: :math:`N` and :math:`n`
.. |txt_N|           replace:: number of discrete-time steps and discrete-time-step counter
.. |eqs_Nb|          replace:: :math:`N_b` and :math:`n_b`
.. |txt_Nb|          replace:: number of rotor blades and blade counter
.. |eqs_Nnp|         replace:: :math:`N_{n_p}^\text{Polar}` and :math:`n^\text{Polar}`
.. |txt_Nnp|         replace:: number of points in the polar grid of wake plane :math:`n_p` and point counter
.. |eqs_NWake|       replace:: :math:`N^\text{Wake}` and :math:`n^\text{Wake}`
.. |txt_NWake|       replace:: number of wakes overlapping a given wind data point in the wind domain and wake counter
.. |eqs_NP|          replace:: :math:`N_P` and :math:`n_P`
.. |txt_NP|          replace:: number of wake planes and wake-plane counter
.. |eqs_Nr|          replace:: :math:`N_r` and :math:`n_r`
.. |txt_Nr|          replace:: number of radial nodes and radii counter
.. |eqs_Nt|          replace:: :math:`N_t` and :math:`n_t`
.. |txt_Nt|          replace:: number of wind turbines and turbine counter
.. |eqs_OF|          replace:: OF
.. |txt_OF|          replace:: OpenFAST (module)
.. |eqs_OpenMP|      replace:: OpenMP
.. |txt_OpenMP|      replace:: open multiprocessing
.. |eqs_pHub|        replace:: :math:`\vec{p}^\text{Hub}`
.. |txt_pHub|        replace:: global position of a rotor center
.. |eqs_pPlane|      replace:: :math:`\vec{p}^\text{Plane}_{n_p}`
.. |txt_pPlane|      replace:: global position of the center of wake plane :math:`n_p`
.. |eqs_RAM|         replace:: RAM
.. |txt_RAM|         replace:: random-access memory
.. |eqs_RSS|         replace:: RSS
.. |txt_RSS|         replace:: root-sum-squared
.. |eqs_r|           replace:: :math:`r` and :math:`r^\text{Plane}`
.. |txt_r|           replace:: radius in the axisymmetric coordinate system
.. |eqs_rPlane|      replace:: :math:`\hat{r}^\text{Plane}`
.. |txt_rPlane|      replace:: radial unit vector in the axisymmetric coordinate system
.. |eqs_S|           replace:: :math:`S`
.. |txt_S|           replace:: global :math:`X`-, :math:`Y`-, and :math:`Z`-coordinate
.. |eqs_SOWFA|       replace:: SOWFA
.. |txt_SOWFA|       replace:: Simulator fOr Wind Farm Applications
.. |eqs_t|           replace:: :math:`t`
.. |txt_t|           replace:: simulation time
.. |eqs_TIAmb|       replace:: :math:`TI_\text{Amb}` and :math:`^\text{Filt}TI_{\text{Amb}_{n_p}}`
.. |txt_TIAmb|       replace:: ambient turbulence intensity of the wind at a rotor and its low-pass time-filtered value for wake plane :math:`n_p`
.. |eqs_ud|          replace:: :math:`u^d`
.. |txt_ud|          replace:: discrete-time inputs
.. |eqs_Vadvect|     replace:: :math:`V_\text{Advect}`
.. |txt_Vadvect|     replace:: advection speed of the synthetic wind data
.. |eqs_VAmbHigh|    replace:: :math:`\vec{V}_\text{Amb}^\text{High}`
.. |txt_VAmbHigh|    replace:: ambient wind across a high-resolution wind domain around a turbine
.. |eqs_VAmbLow|     replace:: :math:`\vec{V}_\text{Amb}^\text{Low}`
.. |txt_VAmbLow|     replace:: ambient wind across a  low-resolution wind domain throughout the wind farm
.. |eqs_VDistHigh|   replace:: :math:`\vec{V}_\text{Dist}^\text{High}`
.. |txt_VDistHigh|   replace:: disturbed wind across a high-resolution wind domain around a turbine
.. |eqs_VDistLow|    replace:: :math:`\vec{V}_\text{Dist}^\text{Low}`
.. |txt_VDistLow|    replace:: disturbed wind across a low-resolution wind domain throughout the wind farm
.. |eqs_VHub|        replace:: :math:`V_\text{Hub}`
.. |txt_VHub|        replace:: mean hub-height wind speed
.. |eqs_Vnp|         replace:: :math:`\vec{V}_{n_p}^\text{Plane}` and :math:`^\text{Filt}\vec{V}_{n_p}^\text{Plane}`
.. |txt_Vnp|         replace:: advection, deflection,  and meandering velocity and its low-pass time-filtered value of wake plane :math:`n_p`
.. |eqs_Vr|          replace:: :math:`V_r`
.. |txt_Vr|          replace:: radial velocity in the axisymmetric coordinate system
.. |eqs_Vrnp|        replace:: :math:`V_{r_{n_p}}^\text{Wake}(r)`
.. |txt_Vrnp|        replace:: radial wake-velocity deficit at wake plane :math:`n_p`, distributed radially
.. |eqs_VTK|         replace:: VTK
.. |txt_VTK|         replace:: Visualization Toolkit
.. |eqs_VxRel|       replace:: :math:`^\text{DiskAvg}V_x^\text{Rel}` and :math:`^\text{FiltDiskAvg}V_x^\text{Rel}`
.. |txt_VxRel|       replace:: rotor-disk-averaged relative wind speed (ambient plus wakes of neighboring turbines plus turbine motion), normal to the disk, and its low-pass time-filtered value
.. |eqs_Vx|          replace:: :math:`V_x`
.. |txt_Vx|          replace:: axial velocity in the axisymmetric coordinate system
.. |eqs_VxnpWake|    replace:: :math:`V_{x_{n_p}}^\text{Wake}(r)`
.. |txt_VxnpWake|    replace:: axial wake-velocity deficit at wake plane :math:`n_p`, distributed radially
.. |eqs_DiskAvgVx|   replace:: :math:`^\text{DiskAvg}V_x^\text{Wind}` and :math:`^\text{FiltDiskAvg}V_{x_{n_p}}^\text{Wind}`
.. |txt_DiskAvgVx|   replace:: rotor-disk-averaged ambient wind speed, normal to the disk, and its low-pass time-filtered value at wake plane :math:`n_p`
.. |eqs_wnWind|      replace:: :math:`w_{n^\text{Wind}}`
.. |txt_wnWind|      replace:: weighting in the spatial averaging for wind data point :math:`n^\text{Wind}`
.. |eqs_WD|          replace:: WD
.. |txt_WD|          replace:: wake dynamics (module)
.. |eqs_WISDEM|      replace:: WISDEM
.. |txt_WISDEM|      replace:: Wind-Plant Integrated System Design & Engineering Model
.. |eqs_xxnp|        replace:: :math:`x` and :math:`x_{n_p}^\text{Plane}`
.. |txt_xxnp|        replace:: downwind distance from a rotor to wake plane :math:`n_p` in the axisymmetric coordinate system
.. |eqs_XYZ|         replace:: :math:`X`, :math:`Y`, and :math:`Z`
.. |txt_XYZ|         replace:: inertial-frame coordinates, with Z directed vertically upward, opposite gravity, X directed horizontally nominally downwind (along the zero-degree wind direction), and Y directed horizontally transversely
.. |eqs_hatXYZ|      replace:: :math:`\hat{X}`, :math:`\hat{Y}`, and :math:`\hat{Z}`
.. |txt_hatXYZ|      replace:: unit vectors of the inertial-frame coordinate system, parallel to the X, Y, and X coordinates
.. |eqs_xd|          replace:: :math:`x^d`
.. |txt_xd|          replace:: discrete-time states
.. |eqs_Xd|          replace:: :math:`X^d(\quad)`
.. |txt_Xd|          replace:: discrete-time state functions
.. |eqs_hatxDisk|    replace:: :math:`\hat{x}^\text{Disk}`
.. |txt_hatxDisk|    replace:: orientation of a rotor centerline
.. |eqs_hatxnpPlane| replace:: :math:`\hat{x}_{n_p}^\text{Plane}`
.. |txt_hatxnpPlane| replace:: orientation of wake plane :math:`n_p`
.. |eqs_yd|          replace:: :math:`y^d`
.. |txt_yd|          replace:: discrete-time outputs
.. |eqs_Yd|          replace:: :math:`Y^d(\quad)`
.. |txt_Yd|          replace:: discrete-time output functions
.. |eqs_zbot|        replace:: :math:`z_\text{bot}`
.. |txt_zbot|        replace:: bottom vertical location of synthetic turbulence inflow grid
.. |eqs_alpha|       replace:: :math:`\alpha`
.. |txt_alpha|       replace:: low-pass time-filter parameter
.. |eqs_DeltaT|      replace:: :math:`\Delta t`
.. |txt_DeltaT|      replace:: discrete time step (increment)
.. |eqs_YawErr|      replace:: :math:`\gamma^\text{YawErr}` and :math:`^\text{Filt}\gamma_{n_p}^\text{YawErr}`
.. |txt_YawErr|      replace:: nacelle-yaw error of a rotor and its low-pass time-filtered value at wake plane :math:`n_p`
.. |eqs_nuT|         replace:: :math:`\nu_T`
.. |txt_nuT|         replace:: eddy viscosity
.. |eqs_rho|         replace:: :math:`\rho`
.. |txt_rho|         replace:: air density
.. |eqs_TwoD|        replace:: 2D
.. |txt_TwoD|        replace:: two dimensional
.. |eqs_ThreeD|      replace:: 3D
.. |txt_ThreeD|      replace:: three dimensional