# 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 $$\delta_\nu$$.