%\mbox{}


% Turbine and blade properties
\nomenclature[T]{$P$}{Turbine power}
\nomenclature[T]{$T$}{Turbine thrust}
\nomenclature[T]{$V_b$}{Turbine blade volume}
\nomenclature[T]{$F_l$}{Lift force}
\nomenclature[T]{$F_d$}{Drag force}
\nomenclature[T]{$\Psi$}{Turbine yaw angle}
\nomenclature[T]{$A_t$}{Swept area of turbine}
\nomenclature[T]{$A_l$}{Turbine local passage cross-sectional area, bounded by a line defined at the midpoint between adjacent turbines}
\nomenclature[T]{$A_c$}{Cross-sectional area of channel}
\nomenclature[T]{$B_g$}{Global blockage defined as $\tfrac{\sum A_t}{A_c}$}
\nomenclature[T]{$B_l$}{Local blockage defined as $\tfrac{A_t}{A_l}$}
\nomenclature[T]{$s$}{Tip-to-tip turbine spacing}
\nomenclature[T]{$D$}{Turbine diameter}
\nomenclature[T]{$\delta$}{Trailing edge thickness}
\nomenclature[T]{$\theta$}{Turbine rotational position}
\nomenclature[T]{$Z_{hub}$}{Depth of the turbine hub}
\nomenclature[T]{$K$}{Resistance coefficient in the porous disc model}
\nomenclature[T]{$F_{tip}$}{Tip correction factor}
\nomenclature[T]{$\Phi$}{Symmetry factor used to quantify bias between inboard and outboard turbines}
\nomenclature[T]{$\eta$}{Basin efficiency defined as the ratio between power extracted from the flow to total power removed from the flow}
\nomenclature[T]{$\alpha$}{Angle of attack}
\nomenclature[T]{$\alpha^*$}{Angle of attack where section lift to drag ratio is a maximum }
\nomenclature[T]{$\beta$}{Blade twist angle}
\nomenclature[T]{$\phi$}{Flow angle between the approach flow and rotor plane (sum of $\alpha$ and $\beta$)}
\nomenclature[T]{$\lambda$}{Tip speed ratio defined as $\tfrac{\Omega R}{u_\infty}$}
\nomenclature[T]{$\lambda^*$}{Tip speed ratio which achieves the highest power coefficient}
\nomenclature[T]{$\lambda_{max}$}{Maximum tip speed ratio prior to the onset of cavitation}
\nomenclature[T]{$f_0$}{Once per-rotation frequency}
% \nomenclature[T]{$c_x$}{Local thrust coefficient at a radial position, $r$, on a turbine blade defined as $\tfrac{\delta F_x}{\tfrac{1}{2} \rho u_x^2 \delta A}$}
\nomenclature[T]{$C_a$}{Cavitation number defined as $\tfrac{p-p_{v}}{\tfrac{1}{2} \rho W^2}$}
\nomenclature[T]{$c_l$}{2D lift coefficient defined as $\tfrac{F_l}{\tfrac{1}{2}\rho W^2 c}$}
\nomenclature[T]{$c_d$}{2D drag coefficient defined as $\tfrac{F_d}{\tfrac{1}{2}\rho W^2 c}$}
\nomenclature[T]{$c_x$}{Stream-wise local thrust coefficient defined as $c_l \cos(\phi) + c_d \sin(\phi)$}
\nomenclature[T]{$c_{\theta}$}{Rotational thrust coefficient defined as $ c_l \sin(\phi) - c_d \cos(\phi)$}
\nomenclature[T]{$c_q$}{Torque coefficient defined as $c_{\theta} r$}
\nomenclature[T]{$C_p$}{Turbine power coefficient defined as $\tfrac{P}{\tfrac{1}{2}\rho A_t u_{\infty}^3}$}
\nomenclature[T]{$C_p^*$}{Maximum turbine power coefficient}
\nomenclature[T]{$C_{pressure}$}{Pressure coefficient defined as $\tfrac{p-p_\infty}{\tfrac{1}{2}\rho W^2}$}
\nomenclature[T]{$C_t$}{Turbine thrust coefficient defined as $\tfrac{T}{\tfrac{1}{2}\rho A_t u_{\infty}^2}$}
\nomenclature[T]{$C_t^*$}{Turbine thrust coefficient at $\lambda^*$}
\nomenclature[T]{$F_x$}{Blade force in the stream-wise direction}
\nomenclature[T]{$F_\theta$}{Blade force in the torque direction}
\nomenclature[T]{$M_{EW}$}{Edge-wise blade root bending moment}
\nomenclature[T]{$M_{FW}$}{Flap-wise blade root bending moment}
\nomenclature[T]{$M_{EW}^*$}{Averaged edge-wise blade root bending moment from thrust and torque transducer}
\nomenclature[T]{$M_{EW}'$}{Edge-wise blade root bending moment corrected for blade self weight}
\nomenclature[T]{$M_{FW}^*$}{Average flap-wise blade root bending moment from thrust and torque transducer}
\nomenclature[T]{$SG$}{Data read from the strain gauge}
\nomenclature[T]{$C$}{Ratio between the moments measured from the thrust and torque transducer to the blade mounted strain gauges}
\nomenclature[T]{$\sigma$}{Blade solidity defined as $\tfrac{N_b c}{2 \pi r}$}
\nomenclature[T]{$c$}{Chord length}
\nomenclature[T]{$R$}{Turbine radius}
\nomenclature[T]{$r$}{Turbine radial position}
\nomenclature[T]{$r_T$}{Radial location of the line of action for thrust on a turbine blade}
\nomenclature[T]{$r_b$}{Radial location of the blade centre of mass}
\nomenclature[T]{$N_b$}{Number of blades per turbine}
\nomenclature[T]{$Q$}{Volumetric flow rate through turbine swept area}
\nomenclature[T]{$Q_{\infty}$}{Free-stream volumetric flow rate through a turbine swept area}



% abbreviations
\nomenclature[A]{RANS}{Reynolds-Averaged Navier-Stokes}
\nomenclature[A]{LMADT}{Linear momentum actuator disc theory}
\nomenclature[A]{BE}{Blade element}
\nomenclature[A]{2D}{Two dimensional}
\nomenclature[A]{3D}{Three dimensional}
\nomenclature[A]{UDF}{User defined function}
\nomenclature[A]{BEM}{Blade element momentum}
\nomenclature[A]{MRF}{Multiple reference frames}
\nomenclature[A]{DNS}{Direct numerical simulation}
\nomenclature[A]{SST}{Shear stress transport}
\nomenclature[A]{CNC}{Computer numerical controlled}
\nomenclature[A]{FFT}{Fast Fourier Transform}
\nomenclature[A]{GR}{Growth rate}

% units and constants
\nomenclature[U]{m}{Meters}
\nomenclature[U]{mm}{Millimetres}
\nomenclature[U]{kg}{Kilograms}
\nomenclature[U]{N}{Newtons}
\nomenclature[U]{g}{Acceleration due to gravity taken as 9.81 m/s}
\nomenclature[U]{$^\circ$}{Degrees}



% \nomenclature{$\delta_{ij}$}{Kronecker delta}


% Physical properties
\nomenclature[P,01]{\(\gamma\)}{Fraction of time where flow is fully turbulent}
\nomenclature[P,02]{\(\epsilon\)}{Dissipation rate of turbulent kinetic energy}
\nomenclature[P,03]{\(\mu\)}{Dynamic viscosity}
\nomenclature[P,04]{\(\nu\)}{Kinematic viscosity defined as $\tfrac{\mu}{\rho}$}
\nomenclature[P,05]{\(\nu_t\)}{Eddy viscosity}
\nomenclature[P,06]{\(\rho\)}{Fluid density}
\nomenclature[P,07]{\(\sigma_{xx}\)}{Normal stresses}
\nomenclature[P,08]{\(\tau_{xy}\)}{Shear stresses}
\nomenclature[P,09]{\(\tau_w\)}{Wall shear stress}
\nomenclature[P,10]{\(\omega\)}{Specific dissipation rate of turbulent kinetic energy}
\nomenclature[P,11]{\(\Omega\)}{Rotational speed in rad/s}
\nomenclature[P]{\(A\)}{Area}
\nomenclature[P]{\(F\)}{Force}
\nomenclature[P]{\(Q_t\)}{Torque}
\nomenclature[P]{\(Re\)}{Reynolds number defined as $\tfrac{\rho u L}{\mu}$ }
% \nomenclature[P]{\(\overline{Re_{\theta,t}}\)}{Momentum thickness Reynolds number}
\nomenclature[P]{\(T_s\)}{Cauchy stress tensor}
\nomenclature[P]{\(TI\)}{Turbulence intensity}
\nomenclature[P]{\(V\)}{Volume}
\nomenclature[P]{\(W\)}{Relative speed of the flow to turbine blade}
\nomenclature[P]{\(k\)}{Turbulent kinetic energy}
\nomenclature[P]{\(m\)}{Mass}
\nomenclature[P]{\(p\)}{Pressure}
\nomenclature[P]{\(p_{atm}\)}{Atmospheric pressure}
\nomenclature[P]{\(p_{section}\)}{Static pressure over an aerofoil section}
\nomenclature[P]{\(p_v\)}{Vapour pressure}
\nomenclature[P]{\(p_z\)}{Pressure at depth z}
\nomenclature[P]{\(u\)}{Velocity vector}
% \nomenclature[P]{\(\overline{u}\)}{Time averaged velocity}
\nomenclature[P]{\(u'\)}{Fluctuating velocity component}
\nomenclature[P]{\(u_{*}\)}{Friction velocity defined as $\sqrt{\frac{\tau_w}{\rho}}$}
\nomenclature[P]{\(u_{\infty}\)}{Free-stream velocity}
\nomenclature[P]{\(u_\theta\)}{Swirl velocity}
\nomenclature[P]{\(u_{norm}\)}{Velocity normal to the turbine}
\nomenclature[P]{\(u_r\)}{Radial velocity}
\nomenclature[P]{\(u_x\)}{Stream-wise velocity}
\nomenclature[P]{\(u_y\)}{Cross-stream velocity}
\nomenclature[P]{\(u_z\)}{Vertical velocity}
\nomenclature[P]{\(y\)}{Wall distance}
\nomenclature[P]{\(y^+\)}{Non-dimensional wall distance defined as $\tfrac{u_{*} y }{\nu}$}
% \nomenclature[P]{\(\overline{y^+}\)}{Area weighted average $y^+$}


\printnomenclature