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Horizontal distribution of the vertically integrated barotropic‐to‐baroclinic energy conversion has been widely studied to examine the generation of internal tides at steep topography. The vertical structure of the energy conversion that provides insights into the associated dynamics, however, is masked by the often used depth‐integrated approach. Here, we reveal the vertical profile of barotropic‐to‐baroclinic energy conversion by employing an idealized ocean model in a slope‐shelf context forced byM₂barotropic tidal flow. The model shows two vertically separated hotspots of energy conversion, one near the sloping bottom and the other at the thermocline, resulting from the stronger vertical velocity and enhancement of the density perturbation, respectively. Isolation of the hotspots demonstrates that baroclinic energy generated in the bottom layer radiates toward onshore and offshore primarily in the form of internal wave beams, whereas that generated at the thermocline propagates away in the form of internal wave modes. Although energy converted at the thermocline contributes to only a small portion of the total energy conversion, it plays an important role in onshore baroclinic energy radiation and can be significantly affected by the internal wave activity at the bottom layer. With a fixed bottom topography, the percentage of baroclinic energy generated at the thermocline is linearly related to a body force exerted by the barotropic tidal flow over topography that can be estimated analytically. This provides a convenient way to estimate the overall barotropic‐to‐baroclinic energy conversion over a continental slope in the real ocean by measuring the energy conversion in the thermocline only.

 

Abstract. Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.