Internal-wave cavity response ($D/{\eta }_i=\sqrt{3}/(2-e^{-2i{m}_{2}H})$)

A reflecting bottom beneath a jump in buoyancy frequency creates a standing field from repeated transmitted and reflected internal gravity waves. For ray angles ${\theta }_1=\pi /3$ and ${\theta }_2=\pi /6$, the downward particle-displacement amplitude has magnitude $\sqrt{3}|{\eta }_i|/[1+8{\sin }^2(m_{2}H){]}^{1/2}$. It reaches $\sqrt{3}|{\eta }_i|$ when $m_{2}H$ is an integer multiple of $\pi$. The upper reflected wave has the same amplitude magnitude as the incident wave because the lossless closed cavity admits no net downward energy flux.