.. _glossary:

Glossary
========

+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| Symbol                        | Definition                                                                                |  Unit             |
+===============================+===========================================================================================+===================+
| :math:`D`                     | Turbine rotor diameter (fixed parameter, :math:`D=27` m)                                  | m                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`t`                     | Time                                                                                      | s                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`t_*`                   | Integral time scale computed from time series at a point                                  | s                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`x, y, z`               | Spatial coordinates, where :math:`x` is aligned with the mean wind                        | m                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`n_t,n_x,n_y,n_z`       | Number points in time and space dimensions                                                | \-                |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`u`                     | Wind vector component along :math:`x`                                                     | m/s               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`v`                     | Wind vector component along :math:`y`                                                     | m/s               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`w`                     | Wind vector component along :math:`z`                                                     | m/s               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`U`                     | Magnitude of horizontal wind speed vector                                                 | m/s               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`v_{los}`               | Wind vector component along the line of sight of each lidar beam                          | m/s               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\beta`                 | Direction of horizontal wind speed vector                                                 | deg               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\Delta \beta`          | Veer computed at fixed :math:`(x,y)` from two distinct :math:`z` points                   | deg               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`TI`                    | Turbulence intensity computed over a 10-min period from horizontal wind speed             | %                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\alpha`                | Power law exponent derived from :math:`U(z=10~\mathrm{m})` and :math:`U(z=58~\mathrm{m})` | \-                |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`u_*`                   | Friction velocity                                                                         | m/s               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\theta`                | Potential temperature                                                                     | K                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\theta_v`              | Virtual potential temperature                                                             | K                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\overline{w'\theta_v'}`| Kinematic vertical turbulent heat flux                                                    | K m/s             |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`L`                     | Obukhov length                                                                            | m                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`z_0`                   | Roughness length                                                                          | m                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`z_i`                   | Atmospheric boundary layer height                                                         | m                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\overline{q}`          | Temporal average of variable :math:`q`                                                    | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\langle q \rangle`     | Ensemble average of variable :math:`q`                                                    | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`q'`                    | Temporal perturbation of variable :math:`q`, defined as :math:`q-\overline{q}`            | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`q_{hub}`               | Variable :math:`q` evaluated at hub height                                                | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`\sigma_q`              | Standard deviation of some quantity :math:`q` (over time, space, or an ensemble)          | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`q_{rotor}`             | Variable :math:`q` evaluated across the rotor in the vertical direction                   | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`q_{wake}`              | Variable :math:`q` evaluated in the wake                                                  | unit of :math:`q` |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`P`                     | Generator power                                                                           | W                 |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`M_y`                   | Out-of-plane bending moment evaluated at the blade root (==flapwise moment)               | N m               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+
| :math:`M_x`                   | In-plane bending moment evaluated at the blade root (==edgewise moment)                   | N m               |
+-------------------------------+-------------------------------------------------------------------------------------------+-------------------+