Wave drag in oscillatory mean flows

In both the atmosphere and ocean, large-scale (mean) flows over topography generate internal waves. A longstanding question in both fields is what forces – often known as ‘wave drag’ – are exerted on the mean flow in this process, as such forces must be parameterized in non-wave-resolving numerical models. For a time-invariant mean flow, it is well known that lee waves are generated which extract momentum from the solid earth and deposit it where they break and dissipate at height. Here, I address the equivalent problem for a time-periodic mean flow (e.g. the ocean tide) using theory and numerical simulations. In this situation, the waves influence the amplitude and phase of the periodic mean flow near the topography regardless of where they dissipate. Dissipation plays a role in terms of controlling the magnitude of wave reflections from an upper boundary (e.g. the ocean surface) which modifies the forces acting near the topography. Our results form a framework for parameterizing tidal internal wave drag in global ocean models.