On the Breaking of Internal Waves in the Ocean

Abstract

Abstract The onset of instability in monochromatic two-dimensional internal near-inertial gravity waves propagating in an ocean of constant buoyancy frequency and no mean shear is examined for increasing values of the wave steepness s, the product of the wave amplitude, and the vertical wavenumber of the waves. Stability of disturbances to the quasi-steady flow depends on the minimum Richardson number of the flow in the direction of the disturbance vector. The minimum Richardson numbers both of the quasi-steady x-directed flow, Jx (that is, in the horizontal direction of wave propagation), and of the transverse y-directed flow, Jy, may be <1/4 for steepness, s < 1, provided that σ/f is sufficiently close to unity, where σ is the wave frequency and f the Coriolis frequency. For waves of increasing steepness but fixed frequency, it is found that the minimum Richardson number of flow in the y direction, Jy, becomes less than 1/4 before those of flows in other directions, suggesting that disturbances in the y...