.. _AA-symbols:

List of Symbols
---------------

+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{l}`                                            +  low frequency                                             +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{h}`                                            +  high frequency                                            +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{p}`                                            +  airfoil pressure side                                     +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{s}`                                            +  airfoil suction side                                      +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{t}`                                            +  turbulence                                                +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{0}`                                            +  reference                                                 +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{1}`                                            +  parallel to airfoil chord                                 +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{2}`                                            +  normal to airfoil chord                                   +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{}_{3}`                                            +  blade spanwise direction                                  +                   +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\alpha`                                            +  angle of attack                                           + [rad]             +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\beta^{2}`                                         +  Prandtl-Glauert correction factor                         + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\delta`                                            +  airfoil boundary layer thickness                          + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\delta^{*}`                                        +  airfoil boundary layer displacement thickness             + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\theta`                                            +  airfoil boundary layer momentum thickness                 + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\Theta_{e},\ \Phi_{e}`                             +  angles between emitter and observer                       + [rad]             +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\rho`                                              +  air density                                               + [kg/m\ :sup:`3`]  +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\omega`                                            +  radial frequency                                          + [rad/s]           +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`A_{w}`                                             +  A-weight                                                  + [dB]              +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`c`                                                 +  speed of sound                                            + [m/s]             +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`c_{i}`                                             +  chord at blade spanwise position i                        + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`d`                                                 +  blade span at station i                                   + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\overline{D}`                                      +  directivity function                                      + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`f`                                                 +  frequency                                                 + [Hz]              +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`G`                                                 +  empirical function                                        + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`h`                                                 +  height of the trailing edge thickness                     + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`H`                                                 +  airfoil kinematic shape factor                            + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`I`                                                 +  turbulence intensity                                      + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`k`                                                 +  wave number                                               + [m\ :sup:`-1`]    +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\overline{k},\ \widehat{k}`                        +  nondimensional wave number                                + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`{\mathrm{\Delta}K_{1},\ K}_{1}`,\ :math:`\ K_{2}`  +  empirical parameters of the BPM model                     + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`l`                                                 +  spanwise extent of the separation zone from blade tip     + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`L`                                                 +  lift force                                                + [N]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`L_{t}`                                             +  length scale                                              + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`M`                                                 +  Mach number                                               + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`M_{c}`                                             +  Mach number past the trailing edge                        + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`r_{e}`                                             +  effective observer distance                               + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\text{Re}`                                         +  Reynolds number                                           + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`S^{2}`                                             +  Sears function                                            + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`\text{St}`                                         +  Strouhal number                                           + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`t_{x}`                                             +  relative thickness of the airfoil at chordwise position x + [-]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`U`                                                 +  local inflow velocity                                     + [m/s]             +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`y`                                                 +  blade spanwise position                                   + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`z`                                                 +  height above the ground                                   + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+
+ :math:`z_{0}`                                             +  ground surface roughness                                  + [m]               +
+-----------------------------------------------------------+------------------------------------------------------------+-------------------+