On the loss of energy from the ocean mesoscale flow via slaved inertia-gravity waves

A recent laboratory experiment of Williams, Haine, and Read (2005; JFM) has observed co-existence of inertia-gravity waves (IGWs) and vortical Rossby waves in a rotating two-layer annular fluid. The IGW amplitudes in the experiments show a broadly linear variation with Rossby number in the range 0.05–0.14, at constant Burger number. We propose and test a dynamical explanation for the source of these IGWs based on the asymptotic renormalization theory of Wirosoetisno, Shepherd, and Temam (2002; JAS), for the limit of small Rossby number. The first-order renormalized equation derived by those authors reduces to quasi-geostrophic dynamics in our case. The renormalized solution also contains a first-order “slaved” term consisting only of IGWs, however. The IGW amplitudes are controlled by the vortical flow, but they oscillate rapidly in time.

We compute the analogue of this slaved term in the particular configuration of the laboratory experiment using results of a two-layer, quasi-geostrophic numerical model. There is good overall agreement with the location and amplitude of the slaved IGWs and the laboratory IGWs, although there are differences in detail. This good agreement strongly suggests that the laboratory waves are slaved to the vortical flow. On this basis, we extrapolate the energy emission into slaved IGWs seen in the experiments to the global ocean energy budget exploiting the Rossby and Burger number scalings implied by the asymptotic theory. We estimate the flux from the balanced mesoscale circulation into IGWs may reach O(1 TW), albeit with substantial uncertainty. This finding suggests that mesoscale energy leakage through slaved IGWs may represent a non-negligible contribution to the global energy budget.