 Internal-wave transmission across a buoyancy-frequency jump

At a jump in buoyancy frequency with continuous background density, incident, reflected and transmitted internal gravity waves share frequency and horizontal wavenumber. Continuity of pressure and normal velocity determines their amplitudes. If amplitudes multiply unit particle-displacement vectors directed along each ray with positive horizontal component, the reflection coefficient is $[\sin {\theta }_2/\sin {\theta }_1-\cos {\theta }_2/\cos {\theta }_1]/[\sin {\theta }_2/\sin {\theta }_1+\cos {\theta }_2/\cos {\theta }_1]$. Using vertical-displacement amplitudes reverses the reflected coefficient's sign because the reflected polarization reverses its vertical component.