A condition on the average Richardson number for weak non-linearity of internal gravity waves

A condition on the average Richardson number, Ri, for weak non-linearity of an internal gravity wavefield is derived using a quasi-normal assumption. For weak non-linearity to be satisfied it is required that Ri⁻¹ « 0.5. This condition is very rarely satisfied in the ocean at vertical scales up to the order of 100 m, for which it is often found that Ri⁻¹ ∼ 1. The analysis suggests that non-linear effects are of no less importance than linear effects in the dynamics of the interior of the ocean at these scales.