Boundary layer at airfoil stagnation points

[charlies1902]

I was reading this:
http://www.creatis.insa-lyon.fr/~dsarrut/bib/Archive/others/phys/www.mas.ncl.ac.uk/%257Esbrooks/book/nish.mit.edu/2006/Textbook/Nodes/chap06/node29.html

Under the first figure it states "Figure 6.20: The boundary layer at a stagnation point on an airfoil has a constant thickness"

Could someone explain to me in which direction is the boundary layer constant? Is it in the x- or z- direction (z- direction being in and out of the screen).

 

[Geofleur]

If I understand correctly, it's constant in both the $x$ and $z$ directions, but for a different reason in each direction. It seems like the flow is assumed invariant to translation along the $z$ axis, similar to how, say, Poiseuille flow is invariant to translation along the axis of the pipe. Moreover, it looks like the fluid velocity along the $z$ direction is assumed to be zero. The fluid is splitting, half of it going in the direction of increasing $x$ and the other half in the direction of decreasing $x$. The boundary layer is constant along the $x$ axis because of the physical process being discussed (stagnation), and not because of some symmetry embedded in the model (though it's not an unreasonable symmetry to expect if the edge of the wing is along the $z$ axis).