= Circular mountain-wave ray in linear shear
{title2=$(x-x_t)^2+(z+H)^2=(H/q_0)^2$}
For a stationary <internal gravity wave> in constant <buoyancy frequency> $N$ and wind $U=U_0(1+z/H)$, set $q_0=kU_0/N<1$. Its upward <group velocity> has ratio $dx/dz=k/m=q/\sqrt{1-q^2}$, where $q=q_0(1+z/H)$. Integrating from the origin gives a circular ray with center $(H\sqrt{1-q_0^2}/q_0,-H)$ and radius $H/q_0$. The ascending ray becomes horizontal at the <turning level of a stationary internal wave>; its reflected branch continues downwind along the same circle.
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