= Internal-wave transmission across a buoyancy-frequency jump
{title2=$\omega=N_j\cos\theta_j$}
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.
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