Rough Topography and Fast Baroclinic Rossby Waves

Oceanographic observations have revealed that basin-scale Rossby waves can travel at speeds systematically exceeding values predicted by linear theory based on the flat-bottom approximation. Using the recently developed parametric "sandpaper" theory of seafloor roughness, we construct a set of analytical solutions for the vertical structure and dispersion relationship of Rossby waves. We then use simulations to confirm these results and show that baroclinic Rossby waves can be accelerated by irregular small-scale (3-30km) $(3-30\,\text{km})$ rough topography by up to a factor of 1.6 relative to their flat-bottom counterparts. This acceleration is most extreme at high latitudes and wavelengths of approximately 600 km. Our investigation demonstrates the importance of relatively small-scale processes for the large-scale flow dynamics in general and baroclinic Rossby waves in particular.