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Sea-floor topography is essential for oceanic fluid dynamics in manyperspectives, and it is believed to enhance energy dissipation to oceanicflows. This study numerically examines the impact of small-scale topography onthe dynamic of quasi-geostrophic barotropic flows and finds thatsmall-amplitude topography enhances upscale energy flux and leads tocondensation, which contradicts the common understanding. Topography-induceddissipation only happens when its amplitude is stronger than the first criticalvalue. And there exists a second critical topography magnitude, correspondingto a second-order phase transition. When the topography magnitude lies betweenthe two critical values, energy simultaneously transfers to both large andsmall scales. When the topography magnitude exceeds the second critical value,energy only transfers downscale. The discovery of counterintuitivetopography-enhanced energy flux and the critical phenomenon brings newchallenges to topography parameterization in ocean models.

Spectral condensation in quasi-geostrophic turbulence above small-scale topography