# Common notationΒΆ

Here we define the notation for several important physical quantities.

\(U_0\) — the freestream streamwise velocity.

\(u_\tau\) — the friction velocity.

\(\nu\) — kinematic viscosity.

\(\delta_\nu\) — the viscous lengthscale, computed as \(\nu/u_\tau\).

\(c_f\) — the skin friction coefficient.

- Measures of the thickness of a boundary layer.

- \(\delta_{99}\) — the location where the mean velocity is equal to \(0.99U_0\).
- \(\delta_*\) — the displacement thickness.
- \(\theta\) — the momentum thickness.

- The velocity field.
\(u, \: v, \: w\) — the streamwise, wall-normal, and spanwise components of the velocity field.

- \(U, \: V, \: W\) — the mean streamwise, wall-normal, and spanwise components of the velocity field.
- \(u', \: v', \: w'\) — the streamwise, wall-normal, and spanwise components of the fluctuations of the velocity field.
Spatial coordinates.

- \(x, \: y, \:, z\) — axes aligned with the streamwise, wall-normal, and spanwise directions.
- \(\eta\) — the wall normal coordinate scaled with the ‘outer scale’, commonly \(\delta_{99}\).
- \(y^+\) — the wall normal coordinate scaled with the viscous lengthscale \(\delta_\nu\).