Rough Topography and Fast Baroclinic Rossby Waves

• Published in: Geophysical research letters Vol. 52; no. 2
• Main Authors: Davis, T. J., Radko, T., Brown, J. M., Dewar, W. K.
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 28.01.2025; Wiley
• Subjects: Acceleration; Approximation; Baroclinic flow; Climate prediction; Exact solutions; Fluid flow; Numerical simulations; Ocean basins; Ocean bottom; Ocean floor; Oceanographic observations; Oceans; phase speed; Planetary waves; Rossby wave; Rossby waves; rough topography; sandpaper; Topography; Vertical profiles; Water flow; Wavelengths; Waves; Weather patterns
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2024GL112589

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. Plain Language Summary Rossby waves are planetary waves that operate on spatial scales of up to those of ocean basins and time scales of up to years. They contribute to climate regulation and communicate changes in weather patterns and ocean flows across the globe. These waves have been the subject of continuous interest since their discovery. However, they usually propagate faster than simplified calculations predict. Several hypotheses have been proposed to explain this discrepancy, attributing it, for instance, to the waves riding on background flow and to large vortices masquerading as Rossby waves. This investigation offers an alternative explanation. We explore the effect a rough ocean bottom can have on the speed of the waves and bring theoretical estimates of the wave's structure and speed into agreement with measurements. We demonstrate that a rough bottom exerts significant drag on the lower part of the wave and causes its upper portion to move faster. Using numerical simulations, we show this acceleration is significant for a wide range of oceanographically relevant parameters. Key Points Observed phase speeds of Rossby waves systematically exceed the prediction of standard linear theory Taking into account the small‐scale variability in the bottom relief brings theoretical estimates of speed close to measurements The effect is most pronounced for extra‐tropical waves with low viscosity and relatively short wavelengths