The three-dimensionality of the triadic resonance instability of a plane inertial wave

Daniel_Andres Mora-Paiba

Given their importance for the weak turbulence theory which aims to describe the small-scale dynamics of the oceanic and atmospheric turbulence, the triadic resonant interactions of internal waves and especially their triadic resonance instability (TRI) have received considerable attention in the last two decades. Nevertheless, previous studies have overlooked a key component of the TRI that we reveal for inertial waves in rotating fluids: the instability produces secondary waves propagating in different vertical planes than the primary wave. In this work, we prove this result theoretically and experimentally. Our observations imply that ensembles of weakly nonlinear inertial waves will quickly reach a statistically axisymmetric state around the rotation axis, which is one of the key assumptions made in the derivation of the weak inertial-wave turbulence theory.