 Prandtl limit

The Prandtl limit observes a high-Reynolds number flow within a shrinking wall-normal layer. For streamwise distance $x$ and outer speed $U$, rescale the normal distance by $\delta =\sqrt{\nu x/U}$ and the normal velocity by $U\delta /x$. Convection and normal viscous diffusion then remain comparable, while streamwise viscous diffusion is smaller. The leading normal momentum equation makes pressure independent of the rescaled normal coordinate, and the tangential equation is the Prandtl boundary-layer equation. This laminar asymptotic balance is local and need not remain valid through separation or instability.