Table of unit conversions

$ \renewcommand{\vec}[1]{ {\bf #1} } \newcommand{\bnabla}{ \vec{\nabla} } \newcommand{\Rey}{Re} \def\vechat#1{ \hat{ \vec{#1} } } \def\mat#1{#1} $

To convert the value of a dimensionless variable in 'code' units to 'lab' units, multiply by $C$ from the following table ('code' units are based on $R$ and $U_{cl}$, 'lab' units are based on $D$ and $U_b$).

E.g. for the variable $z$: $~~z_\mathrm{lab} \,(D) = z_\mathrm{code} \,(R) = z_\mathrm{code} \,(\frac{1}{2}D) ~~\Rightarrow~~z_\mathrm{lab} = z_\mathrm{code} \times \frac{1}{2},~~$ i.e. $z_\mathrm{lab} = z_\mathrm{code} \times C$ with $C=\frac{1}{2}$.

$\begin{array}{ccccl} variable & \mbox{'code' units} & \mbox{'lab' units} & \mbox{conversion factor}~C & \mbox{comment}\\ \hline r,z & R & D & \frac{1}{2} & \mbox{length}\\ \vec{u} & U_{cl} & U_b & 2 & \mbox{speed} \\ t & R/U_{cl} & D/U_b & \frac{1}{4} & \mbox{time} \\ \sigma & U_{cl}/R & U_b/D & 4 & \mbox{growth rate} \\ E & \rho\,U_{cl}^2\, R^3 & \rho\,U_b^2\,D^3 & \frac{1}{2} & \mbox{kinetic energy} \\ D & \rho\,U_{cl}^3\, R^2 & \rho\,U_b^3\,D^2 & 2 & \mbox{dissipation rate} \\ E' & \rho\,U_{cl}^2\, R^2 & \rho\,U_b^2\,D^2 & 1 & \mbox{energy per unit length} \\ \tilde{E} & \rho\,U_{cl}^2 & \rho\,U_b^2 & 4 & \mbox{energy density} \end{array}$