Vertical trapping of an internal gravity wave by planar strain
= Vertical trapping of an internal gravity wave by planar strain
For the planar strain $\mathbf U=\gamma(x,0,-z)$, an internal-wave ray has
$$
k=k_0e^{-\gamma t},
\qquad
m=m_0e^{\gamma t}.
$$
If it initially propagates upward with $m_0<0$, its height remains positive at finite time but decays to zero exponentially as $t\to\infty$.