Appears in collection : 2026 - T2 - WS2 - Instabilities and transitions in geophysical flows

Stably stratified fluids (e.g., oceans and atmosphere) support internal waves that are fundamental to oceanic circulation and atmospheric dynamics. We present the first rigorous proof of instability for small-amplitude internal waves, establishing the existence of an unstable spectrum for the Boussinesq equations linearised about a traveling wave. The analysis combines a Floquet–Bloch decomposition with a variant of Kato’s similarity transformation, exploiting the wave’s structure. In a specific regime, the resulting growth rates agree with previous theoretical predictions for Triadic Resonant Instability of internal waves.