5-wave interactions in inertia-gravity waves

In oceans, multiple energetic inertia-gravity waves often coexist in a region. In this paper, we study the stability of two coexisting plane inertia-gravity waves (hereafter, primary waves), with the same frequencies ($\omega_1$) and wavevector norms, in a region of constant background stratification (denoted by $N$). Specifically, we explore the decay of two primary waves through triadic resonant instabilities (TRIs) in cases where the primary waves do not resonantly interact with each other. Two coexisting primary waves undergoing triadic resonant instability can force two secondary waves each, and this results in two 3-wave systems (3WS). In some cases, two primary waves can have a common secondary wave, and this results in a 5-wave system (5WS) composed of two different triads. We show that 5WSs are the dominant instabilities with higher growth rates than standard triads for a wide range of Coriolis frequency values ($f$). For 2D cases, 5WSs have higher growth rates than triads for $f/\omega_1\gtrapprox0.3$ and for primary waves with the same horizontal (vertical) wavenumber but with opposite vertical (horizontal) wavenumber. Similar results are observed for 3D cases where the primary waves are not on the same vertical plane. Numerical simulations match the theoretical growth rates of 5WSs for a wide range of latitudes, except when $f/\omega_1\approx0.5$ (critical latitude). Using theory and simulations, we show that the maximum growth rate near the critical latitude is approximately twice the maximum growth rate of all triads.