\section*{Nomenclature}
\begin{tabbing}
  XXXXXX \= \kill% this line sets tab stop
  \\
  $\textbf{B}$ \> Magnetic induction field, $T \ (Wb/m^{2})$ \\
  $\textbf{B}_{o}$ \> Applied magnetic field, $T \ (Wb/m^{2})$ \\
  $\textbf{D}$ \> Electric displacement field, $C/m^{2}$ \\
  $\textbf{E}$ \> Electric field, $N/C \ (V/m)$; Global kinetic energy, $J$ \\
  $\textbf{H}$ \> Magnetic field, $A/m$ \\
  $\textbf{j}$ \> Current density, $A/m^{2}$; Jacobian matrix \\
  $\textbf{M}$ \> Magnetization density, $J/(T \ m^{3})$ \\
  $\textbf{P}$ \> Polarization density, $C/m^{2}$; Probability; Particle momentum, $J \cdot s /m$ \\
  $\textbf{T}$ \> Maxwell stress tensor, $N/m^{2}$ \\
  $\textbf{V}$ \> Electric potential, $V$ \\
  $A$ \> Cross sectional area, $m^{2}$ \\
  $C$ \> Contraction coefficient; Discharge coefficient; Constant; Circumference, $m$; \\
         \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Gladstone-Dale constant \\
  $D$ \> Diameter of jet, $m$; Vertical jet height, $m$; Energy dissipation, $J/s$; \\
  $D_{p}$ \> Dispersion function, $m$ \\
  $E_{b}$ \> Proton beam energy, $eV$ \\
  $E_{p}$ \> Energy deposition, $J/g$ \\
  $G$ \> Pressure ratio; Gruneisen coefficient \\
  $I_{T}$ \> Initial intensity of light, $cd$ \\
  $I_{o}$ \> Intensity of light at screen, $cd$ \\
  $K$ \> Loss coefficient; Bulk modulus, $N/m^{2}$ \\
  $L$ \>  Characteristic length, $m$; Pipe length, $m$; Disruption length, $m$ \\
  $L^{disruption}$ \>  Disruption length, $m$ \\
  $M$ \> Mass, $kg$; Molar mass, $g/mol$  \\
  $N_{p}$ \>  Number of protons \\
  $P$ \> Pressure, $N/m^{2}$; Probability; Momentum, $eV/c$  \\
  $P_{p}$ \> Pressure by energy deposition, $N/m^{2}$  \\
  $Q$ \> Flow rate, $m^{3}/s$ \\
  $R$ \> Gas constant, $J/(K \ mol)$; Radius of curvature of the centerline of elbow, $m$ \\
  $T$ \> Temperature, $^{\circ} \mathrm{C} \ (K)$ \\
  $Tp$ \> Tera-protons, $1 \times 10^{12}$ protons \\
  $U$ \> Mean velocity in the \textit{x} coordinate direction, $m/s$ \\
  $V$ \> Volume, $m^{3}$ \\
  $\alpha_{v}$ \> Volume coefficient of thermal expansion, $K^{-1}$ \\
  $\beta$ \> Ratio of diameter, Relativistic function \\
  $\gamma$ \> Ratio of specific heats, $c_{p}/c_{v}$; Relativistic function  \\
  $\Gamma$ \> Surface tension, $N/m$ \\
  $\delta$ \> Kronecker delta; Boundary layer thickness, $m$ \\
  $\epsilon$ \> Amplitude of a sinusoidal wave, $m$; Random error \\
  $\varepsilon$ \> Electrical permittivity, $F/m \ (C^{2}/(N  \ m^{2}))$; Emittance \\
  $\varepsilon_{o}$ \> Electrical permittivity of free space, $F/m \ (C^{2}/(N \ m^{2}))$ \\
  $\zeta$ \> Intermittency factor \\
  $\eta$ \>  Absolute viscosity, $kg/(m \ s)$ \\
  $\theta $ \> Angle, degree \\
  $\kappa$ \> Compressibility, $ m^{2}/N$ \\
  $\lambda$ \> Wavelength of a sinusoidal wave, $m$ \\
  $\mu$ \> Magnetic permeability, $H/m \ (N/A^{2})$ \\
  $\mu_{o}$ \> Magnetic permeability of free space, $H/m \ (N/A^{2})$ \\
  $\nu$ \>  Kinematic viscosity, $\eta/\rho$, $m^{2}/s$ \\
  $\xi$ \> Free surface perturbation, $m$ \\
  $\rho$ \> Density, $kg/m^{3}$ \\
  $\sigma$ \> Electrical conductivity, $S/m$; Standard deviation \\
  $\tau$ \> Joule damping term, $s$; Wall shear stress, $N/m^{2}$\\
  $\phi$ \> Velocity potential, $m^{2}/s$; Angle, degree \\
  $\phi_{E}$ \> Electric potential, $V$ \\
  $\chi_{e}$ \> Electrical susceptibility  \\
  $\chi_{m}$ \> Magnetic susceptibility \\
  $\psi$ \> Stream function, $m^{2}/s$ \\
  $\omega$ \> Vorticity, $s^{-1}$ \\
  $a$ \> Radius of circular pipe, $m$; Radius of jet, $m$ \\
  $c$ \> Local speed of sound, $m/s$; Distance $m$; Wave velocity, $m/s$ \\
  $c_{p}, c_{v}$ \> Specific heat capacity, $J/(g \ K)$ \\
  $d$ \> Diameter of circular pipe, $m$; Diameter of nozzle, $m$; Distance, $m$ \\
  $e$ \> Specific internal energy, $J/kg$; Surface roughness, $m$; Error, $\%$  \\
  $f$ \> Focal length, $m$; Force, $N$; Friction factor \\
  $g$ \> Gravitational constant, $m/s^{2}$ \\
  $h$ \> Head loss, $m$ \\
  $k$ \> Boltzmann constant; Number of parameters \\
  $n$ \> Index of refraction; Experimental data points \\
  $p$ \> Pressure, $N/m^{2}$; Particle momentum, $J \cdot s /m$ \\
  $r$ \> Residual; Radial coordinate \\
  $s$ \> Position \\
  $t$ \> Time, $s$ \\
  $\textit{v}$ \> Directional fluid velocity, $m/s$; Mean velocity, $m/s$ \\
  $\textit{x, y, z}$ \> Cartesian coordinates, $m$ \\
  $\textrm{Al}$ \>  Alfv$\grave{e}$n Number \\
  $\textrm{Fr}$ \> Froude number \\
  $\textrm{Ha}$ \> Hartmann number \\
  $\textrm{N}$ \> Stuart number; Number of events; Augmented Jacobian matrix \\
  $\textrm{Pr}_{m}$ \> Magnetic Prandtl number \\
  $\textrm{Re}$ \> Reynolds number \\
  $\textrm{Re}_{m}$ \> Magnetic Reynolds number \\
  $\textrm{We}$ \> Weber number \\
  $\Delta$ \> Difference \\
  $\nabla \cdot$ \> Divergence operator \\
  $\nabla \times$ \> Curl operator \\
  $\times$ \> Cross product operator \\
  $\cdot$ \> Inner product operator; Multiplication \\
%  $\textrm{Bt}$ \> Batchelor number \\
% $\textit{d}$ \> Wall thickness \\
%  $R$ \> Gas constant \\
%  $\textrm{S}$ \> Sensitivity \\
%  $\textbf{v}$ \> Fluid velocity vector\\
%  $v_{o}$ \> Constant fluid velocity \\
%  $\beta$ \> Amplitude function \\
%  $\kappa$ \> Electrical conductivity, $S/m$ \\
%  $\beta$ \> Amplitude function \\
%  $t$ \> Time \\
%  $\sigma_{o}$ \> Electrical conductivity of wall \\
%  $\textrm{C}_{f}$ \> Friction coefficient \\
%  $\tau$ \> Wall shear stress \\
%  $L_{o}$ \> Intact length of jet \\
%  $\tau_{xy}$ \> Shear stress in the (\textit{x,y}) coordinate direction \\
%  $\textrm{Z}$ \> Total energy \\
%  $E_{v} $ \> Bulk modulus,  \\
%  $\textrm{q}$ \> Heat flux vector \\
%  $\textit{R}_{\textit{b}}$ \> Magnetic force (or pressure) number \\
%  $\ \textrm{Pr} $ \>  Prandtl number \\
%  $\textit{M}$ \> Mach number \\
%  $\gamma$ \> Ratio of specific heats \\
%  $n$ \> Distance along the inward normal \\
%  $L$ \> Characteristic length; Luminosity; Pipe length \\
%  $k_{z}$ \> wave number in the streamwise direction \\
%  $m$ \> wave number in the azimuthal direction \\
%  $\textit{u}, \textit{v}, \textit{w}$ \> Cartesian velocity components \\
%  $\textit{u}_{o}, \textit{v}_{o}, \textit{w}_{o}$ \> Cartesian mean flow velocity components over cross section area \\
\\
\textit{\textbf{Superscripts}} \\
\\
%  $-$ \> Time mean \\
  $'$ \> Differentiation with respect to variable; Perturbation; Fluctuation \\
  $\cdot$ \> Differentiation with respect to time \\

\\
\textit{\textbf{Subscripts}} \\
\\
  $I$ \> Ion thermal \\
  $R$ \> Reference location \\
  $T$ \> Transpose of matrix \\
  $a$ \> Air \\
  $b$ \> Beam \\
  $c$ \> Compression \\
  $e$ \> Electron thermal \\
  $l$ \> Liquid \\
  $\textit{o}$ \> Component mean value; Initial value at the nozzle \\
  $sc$ \> At screen position \\
  $\textit{x, y, z}$ \> Component values in cartesian coordinates \\
  $\perp$ \> Perpendicular direction \\
%  $\textit{l} $ \> The edge of the sublayer \\
%  $avg $ \> Component average value \\
%  $w$ \> Component value at surface wave \\
%  $e$ \> Component value at the edge of the turbulent boundary layer \\
%  $c$ \> Component value at the local core of the cross section \\

\end{tabbing}
