Spectral condensation and bidirectional energy transfer in quasi-geostrophic turbulence above small-scale topography

Abstract

Seafloor topography is essential for oceanic fluid dynamics from many perspectives, and it is believed to enhance energy dissipation in oceanic flows. This study numerically examines the impact of small-scale topography on the dynamics of quasi-geostrophic barotropic flows and finds three regimes and two critical values of topographic magnitude. In the first regime, where the topographic magnitude is below the first critical value, small-amplitude topography extends the range of upscale energy flux and enhances condensation, contradicting the common understanding of topographic damping. In the second regime, where the topography magnitude lies between the two critical values, energy simultaneously transfers to both large and small scales, and topography induces extra dissipation at the topographic scale. A second critical topography magnitude exists, corresponding to a second-order phase transition. When the topography magnitude exceeds the second critical value, energy only transfers downscale. The discovery of counterintuitive topography-enhanced energy flux and its critical phenomenon brings new challenges to topography parameterization in ocean models.