====== fieldprops ======
print out basic properties of a FlowField
options :
-g --geometry show geometrical properties
-m --mean show mean properties
-n --norm show norm properties
-sp --spectral show spectral properties
-sy --symmetry show symmetry properties
-d --dynamic show dynamical properties
-e --energy show energy properties
-R --Reynolds default == 400 Reynolds number
-eps --eps default == 1e-07 spectral noise floor
-dt --dt default == 0.03125 integration time for du/dt estimate
-T --T default == 0.03125 integration time for du/dt estimate
-nl --nonlinearity default == rot method for u grad u [rot or skw]
-dg --digits default == 6 digits of output for reals
(trailing arg 1) input field
Definitions: The norms and energy measures reported by the -n and -e options are defined as follows
$ \begin{align*}
\text{L2Norm} \quad \|u\| &= \left(\frac{1}{L_x L_y L_z} \int_{\Omega} \|{\bf u}\|^2\,\, d{\bf x} \right)^{1/2}\\
\text{energy} \quad E(u) &= \frac{1}{2 L_x L_y L_z} \int_{\Omega} \|{\bf u}\|^2\,\, d{\bf x} \\
\text{dissipation} \quad D(u) &= \frac{1}{L_x L_y L_z} \int_{\Omega} \|\nabla \times {\bf u}\|^2 \,\, d{\bf x} \\
\text{forcing} \quad I(u) &= \frac{1}{L_x L_z} \int_{y=a,b} \frac{\partial u}{\partial y} \, dx dz
\end{align*} $
FIXME: Some of the measures output by fieldprops assume that the field is the fluctuating velocity field
of plane Couette flow, and some quantities are reported for the total velocity field %%u+U%% where %U(y) = y%%.
There should be an option for specifying other common base-flow / fluctuation decompositions, or none.