= Solution
Choose $x$ downslope along the rigid plane and $z$ normal to it into the fluid, with the wall at $z=0$ and the flat free surface at $z=h$. The gravitational <body force> per unit volume has components $(\rho g\sin\alpha,-\rho g\cos\alpha)$. The wind's tangential <traction> on the top surface is $-S$ in the $x$ direction; the atmospheric normal <traction> is $-p_{\rm atm}$ in the $z$ direction. At the wall there is <no-slip boundary condition>, and the wall supplies the opposing normal force and a tangential <traction> whose sign depends on the wind strength.
The velocity is parallel to the plane, $(u(z),0)$. Its <velocity profile> is a concave quadratic, with $u(0)=0$ and negative slope at the free surface when $S>0$. The diagram uses moderate wind, for which the flow is still everywhere downslope. Stronger wind can reverse the upper portion, or the entire moving layer; the later cases quantify this.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ib/paper-1-inclined-film.png]
{title=Coordinates, gravity, surface tractions and a moderate-wind velocity profile}
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