Kinetic Energy Exchanges between a Two-Dimensional Front and Internal Waves

Fronts and near-inertial waves (NIWs) are energetic motions in the upper ocean that have been shown to interact and provide a route for kinetic energy (KE) dissipation of balanced oceanic flows. In this paper, we study these KE exchanges using an idealized model consisting of a two-dimensional geostrophically balanced front undergoing strain-induced semigeostrophic frontogenesis and internal wave (IW) vertical modes. The front–IW KE exchanges are quantified separately during two frontogenetic stages: an exponential sharpening stage that is characterized by a low Rossby number and is driven by the imposed strain (i.e., mesoscale frontogenesis), followed by a superexponential sharpening stage that is characterized by an O(1) Rossby number and is driven by the convergence of the secondary circulation (i.e., submesoscale frontogenesis). It is demonstrated that high-frequency IWs quickly escape the frontal zone and are very efficient at extracting KE from the imposed geostrophic strain field through the deformation shear production (DSP). Part of the extracted KE is then converted to wave potential energy. On the contrary, NIWs remain locked to the frontal zone and readily exchange energy with the ageostrophic frontal circulation. During the exponential stage, NIWs extract KE from the geostrophic strain through DSP and transfer it to the frontal secondary circulation via the ageostrophic shear production (AGSP) mechanism. During the superexponential stage, a newly identified mechanism, convergence production (CP), plays an important role in the NIW KE budget. The CP transfers KE from the convergent ageostrophic secondary circulation to the NIWs and largely cancels out the KE loss due to the AGSP. This CP may explain previous findings of KE transfer enhancement from balanced motions to IWs in frontal regions of realistic ocean models. We provide analytical estimates for the aforementioned energy exchange mechanisms that match well the numerical results. This highlights that the strength of the exchanges strongly depends on the frontal Rossby and Richardson numbers.