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 \(\delta_\nu\).