Breaking of Progressive Internal Gravity Waves: Convective Instability and Shear Instability*

Abstract The breaking of a monochromatic two-dimensional internal gravity wave is studied using a newly developed spectral/pseudospectral model. The model features vertical nonperiodic boundary conditions that ensure a realistic simulation of wave breaking during the wave propagation. Isopycnal overturning is induced at a local wave steepness of sc = 0.75–0.79, which is below the conventional threshold of s = 1. Isopycnal overturning is a sufficient condition for subsequent wave breaking by convective instability. When s = sc, little primary wave energy is being transferred to high-mode harmonics. Beyond s = 1, high-mode harmonics grow rapidly. Primary wave energy is more efficiently transferred by waves of lower frequency. A local gradient Richardson number is defined as Ri = −(g/ρ0)(dρ/dz)/ζ2 to isolate convective instability (Ri ≤ 0) and wave-induced shear instability (0 < Ri < 0.25), where dρ/dz is the local vertical density gradient and ζ is the horizontal vorticity. Consistent with linear wave theor...