Common notation¶
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 \(\delta_\nu\).