# Diagnostic fields¶

Some stand-alone functions are available in the `diagnostics.py`

file
for computing flow diagnostics.

## Courant number¶

The Courant number diagnostic computes the field defined by

\[\frac{||\mathbf{u}||\Delta t}{\Delta x},\]

where \(\Delta t\) is the time-step size and \(\Delta x\) is the element size (more specifically, it is twice the element’s circumradius).

## Grid Reynolds number¶

The Reynolds number (whose length scale is relative to the element size \(\Delta x\)) is defined by

\[\mathrm{Re} = \frac{\rho||\mathbf{u}||\Delta x}{\mu},\]

where \(\rho\) is the fluid density, \(\mu\) is the dynamic viscosity, and \(||\mathbf{u}||\) is the magnitude to the velocity field. Alternatively,

\[\mathrm{Re} = \frac{||\mathbf{u}||\Delta x}{\nu},\]

where \(\nu\) is the kinematic viscosity.

## Divergence¶

This diagnostic field computes the divergence

\[\nabla\cdot\mathbf{u},\]

of a vector field \(\mathbf{u}\).