Modal decomposition of polychromatic internal wave fields in arbitrary stratifications

Internal waves such as those produced by tidal sloshing over seafloor topography play an important role in the energy budget of the oceanic overturning circulation. Understanding their spatial and temporal structure, which depend on both the details of the forcing topography and the forcing frequency, is relevant in predicting how and where wave breaking and mixing may occur. Past work has largely focused on the case of a monochromatic wave field; however, the forcing tides may be composed of multiple frequency constituents. Here we present an approach by which the vertical mode structure of a polychromatic internal wave field may be computed from velocity timeseries data without any a priori knowledge of the details of the forcing topography. We consider wave fields in both uniform and vertically-varying stratification, and show using synthetic data that our approach is able to accurately reconstruct the vertical mode strengths. The sensitivity of our approach to noise and vertical resolution is also examined.