= Internal-wave ray in uniform vertical shear
{title2=$m(t)=m_0-kst,\quad z(t)=(\omega-\widehat\omega(t))/(ks)$}
For $U=sz$, $N>0$, $k>0$ and the rising branch $m_0<0$, the Hamiltonian is $\omega=ksz+Nk/\sqrt{k^2+m^2}$. It gives constant $\omega,k$ and $m=m_0-kst$. The height approaches $z_c=\omega/(ks)$ as time tends to infinity. With $\theta=\arctan(|m|/k)$, the ray slope is $dx/dz=\tan\theta+ksz/(N\sin\theta\cos^2\theta)$. The intrinsic and absolute frequencies must not be confused.
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