# 4.2.14.1. Nomenclature¶

 ABLSolver atmospheric boundary layer solver AWAE ambient wind and array effects (module) $$a(r)$$ axial induction factor, distributed radially $$a_K$$ coherence decrement parameter BEM blade-element momentum $$b_K$$ coherence offset parameter $$C^\text{O}_\text{HWkDfl}$$, $$C^\text{OY}_\text{HWkDfl}$$, $$C^\text{x}_\text{HWkDfl}$$, and $$C^\text{xY}_\text{HWkDfl}$$ calibrated parameters in the horizontal wake-deflection correction $$c_\text{max}$$ maximum blade chord length $$C_\text{Meander}$$ calibrated parameter for wake meandering $$C_\text{NearWake}$$ calibrated parameter in the near-wake correction $$C_\text{WakeDiam}$$ calibrated parameter in the wake-diameter calculation $$C^\text{DMax}_{\nu \text{Amb}}$$, $$C^\text{DMin}_{\nu \text{Amb}}$$, $$C^\text{Exp}_{\nu Amb}$$, and $$C^\text{FMin}_{\nu Amb}$$ calibrated parameters in the eddy-viscosity filter function for ambient turbulence $$C^\text{DMax}_{\nu \text{Shr}}$$, $$C^\text{DMin}_{\nu \text{Shr}}$$, $$C^\text{Exp}_{\nu \text{Shr}}$$, and $$C^\text{FMin}_{\nu \text{Shr}}$$ calibrated parameters in the eddy-viscosity filter function for the wake shear layer $$^\text{AzimAvg}C_t(r)$$ and $$^\text{FiltAzimAvg}C_t(r)$$ azimuthally averaged thrust-force coefficient (normal to a rotor disk), distributed radially, and its low-pass time-filtered value $$Coh_{i,j}$$ magnitude of partial coherence between points $$i$$ and $$j$$ DLL dynamic-link library DWM dynamic wake meandering $$D_\text{Grid}$$ Assumed rotor diameter when generating TurbSim inflow $$D^\text{Rotor}$$ and $$^\text{Filt}D_{n_p}^\text{Rotor}$$ rotor diameter and its low-pass time-filtered value at wake plane $$n_p$$ $$D_{n_p}^\text{Wake}$$ wake diameter at wake plane $$n_p$$ FLORIS FLOw Redirection and Induction in Steady state $$f$$ frequency $$f_c$$ cutoff (corner) frequency of the low-pass time filter $$\vec{f}_{n_b}(r)$$ aerodynamic applied loads distributed radially per unit length for blade $$n_b$$ $$f_\text{max}$$ maximum excitation frequency $$F_{\nu \text{Amb}}(x)$$ eddy-viscosity filter function associated with ambient turbulence $$F_{\nu \text{Shr}}(x)$$ eddy-viscosity filter function associated with the wake shear layer HFM high-fidelity modeling HPC high-performance computer $$I$$ three-by-three identify matrix $$K$$ velocity components $$u$$, $$v$$, and $$w$$ $$k_{\nu \text{Amb}}$$ calibrated parameter for the influence of ambient turbulence in the eddy viscosity $$k_{\nu \text{Shr}}$$ calibrated parameter for the influence of the wake shear layer in the eddy viscosity LES large-eddy simulation MFoR moving frame of reference MPI message-passing interface NaN not a number NREL National Renewable Energy Laboratory $$N$$ and $$n$$ number of discrete-time steps and discrete-time-step counter $$N_b$$ and $$n_b$$ number of rotor blades and blade counter $$N_{n_p}^\text{Polar}$$ and $$n^\text{Polar}$$ number of points in the polar grid of wake plane $$n_p$$ and point counter $$N^\text{Wake}$$ and $$n^\text{Wake}$$ number of wakes overlapping a given wind data point in the wind domain and wake counter $$N_P$$ and $$n_P$$ number of wake planes and wake-plane counter $$N_r$$ and $$n_r$$ number of radial nodes and radii counter $$N_t$$ and $$n_t$$ number of wind turbines and turbine counter OF OpenFAST (module) OpenMP open multiprocessing $$\vec{p}^\text{Hub}$$ global position of a rotor center $$\vec{p}^\text{Plane}_{n_p}$$ global position of the center of wake plane $$n_p$$ RAM random-access memory RSS root-sum-squared $$r$$ and $$r^\text{Plane}$$ radius in the axisymmetric coordinate system $$\hat{r}^\text{Plane}$$ radial unit vector in the axisymmetric coordinate system $$S$$ global $$X$$-, $$Y$$-, and $$Z$$-coordinate SC super controller (module) SOWFA Simulator fOr Wind Farm Applications $$t$$ simulation time $$TI_\text{Amb}$$ and $$^\text{Filt}TI_{\text{Amb}_{n_p}}$$ ambient turbulence intensity of the wind at a rotor and its low-pass time-filtered value for wake plane $$n_p$$ $$u^d$$ discrete-time inputs $$V_\text{Advect}$$ advection speed of the synthetic wind data $$\vec{V}_\text{Amb}^\text{High}$$ ambient wind across a high-resolution wind domain around a turbine $$\vec{V}_\text{Amb}^\text{Low}$$ ambient wind across a low-resolution wind domain throughout the wind farm $$\vec{V}_\text{Dist}^\text{High}$$ disturbed wind across a high-resolution wind domain around a turbine $$\vec{V}_\text{Dist}^\text{Low}$$ disturbed wind across a low-resolution wind domain throughout the wind farm $$V_\text{Hub}$$ mean hub-height wind speed $$\vec{V}_{n_p}^\text{Plane}$$ and $$^\text{Filt}\vec{V}_{n_p}^\text{Plane}$$ advection, deflection, and meandering velocity and its low-pass time-filtered value of wake plane $$n_p$$ $$V_r$$ radial velocity in the axisymmetric coordinate system $$V_{r_{n_p}}^\text{Wake}(r)$$ radial wake-velocity deficit at wake plane $$n_p$$, distributed radially VTK Visualization Toolkit $$^\text{DiskAvg}V_x^\text{Rel}$$ and $$^\text{FiltDiskAvg}V_x^\text{Rel}$$ 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 $$V_x$$ axial velocity in the axisymmetric coordinate system $$V_{x_{n_p}}^\text{Wake}(r)$$ axial wake-velocity deficit at wake plane $$n_p$$, distributed radially $$^\text{DiskAvg}V_x^\text{Wind}$$ and $$^\text{FiltDiskAvg}V_{x_{n_p}}^\text{Wind}$$ rotor-disk-averaged ambient wind speed, normal to the disk, and its low-pass time-filtered value at wake plane $$n_p$$ $$w_{n^\text{Wind}}$$ weighting in the spatial averaging for wind data point $$n^\text{Wind}$$ WD wake dynamics (module) WISDEM Wind-Plant Integrated System Design & Engineering Model $$x$$ and $$x_{n_p}^\text{Plane}$$ downwind distance from a rotor to wake plane $$n_p$$ in the axisymmetric coordinate system $$X$$, $$Y$$, and $$Z$$ 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 $$\hat{X}$$, $$\hat{Y}$$, and $$\hat{Z}$$ unit vectors of the inertial-frame coordinate system, parallel to the X, Y, and X coordinates $$x^d$$ discrete-time states $$X^d(\quad)$$ discrete-time state functions $$\hat{x}^\text{Disk}$$ orientation of a rotor centerline $$\hat{x}_{n_p}^\text{Plane}$$ orientation of wake plane $$n_p$$ $$y^d$$ discrete-time outputs $$Y^d(\quad)$$ discrete-time output functions $$z_\text{bot}$$ bottom vertical location of synthetic turbulence inflow grid $$\alpha$$ low-pass time-filter parameter $$\Delta t$$ discrete time step (increment) $$\gamma^\text{YawErr}$$ and $$^\text{Filt}\gamma_{n_p}^\text{YawErr}$$ nacelle-yaw error of a rotor and its low-pass time-filtered value at wake plane $$n_p$$ $$\nu_T$$ eddy viscosity $$\rho$$ air density 2D two dimensional 3D three dimensional