  Sea-floor topography is essential for oceanic fluid dynamics in many
perspectives, and it is believed to enhance energy dissipation to oceanic
flows. This study numerically examines the impact of small-scale topography on
the dynamic of quasi-geostrophic barotropic flows and finds that
small-amplitude topography enhances upscale energy flux and leads to
condensation, which contradicts the common understanding. Topography-induced
dissipation only happens when its amplitude is stronger than the first critical
value. And there exists a second critical topography magnitude, corresponding
to a second-order phase transition. When the topography magnitude lies between
the two critical values, energy simultaneously transfers to both large and
small scales. When the topography magnitude exceeds the second critical value,
energy only transfers downscale. The discovery of counterintuitive
topography-enhanced energy flux and the critical phenomenon brings new
challenges to topography parameterization in ocean models.
