Forced-Dissipative Two-Layer Quasigeostrophic Waves, Instability, and Turbulence over an Aligned Sloping Bottom

Bottom topography affects ocean turbulence across a vast range of temporal and spatial scales. Here, we show that, outside of the tropics, the ocean’s most energetic regions have large-scale topographic potential vorticity (PV) gradients aligned with background vertical-shear PV gradients. We investigate such aligned bottom slopes of varying sign and magnitude using forced-dissipative two-layer quasigeostrophic (QG) simulations. In two-layer QG turbulence, small-to-moderate bottom slopes support topographic wave energization, while moderate-to-large bottom slopes support cascade arrest, jet formation, and surface-intensified baroclinic waves. Topographic waves are not energized over steep bottom slopes, since the flow is arrested by linear waves at scales smaller than those of topographic waves. Eastward-prescribed flow and emergent jets over bottom slopes that support eastward (westward) topographic wave propagation are prograde (retrograde). Retrograde jets are persistent and self-maintaining, while prograde jets are transient. We show that both jet types act as waveguides, using frequency–wavenumber energy spectra and dispersion relations that account for the emergent zonal-mean jet flow. For a given bottom slope magnitude, prograde-prescribed flows have smaller characteristic length scales than retrograde-prescribed flows, which is rationalized using the Doppler shift of the linear wave modes. Linear wave theory is also used to predict the length scale of the maximum diagnosed turbulent time scale. Last, we suggest two (unclosed) methods for predicting zonal eddy kinetic energy levels and length scales. These results inform both fundamental theory of baroclinic turbulence over a bottom slope and topography-aware parameterizations of ocean eddies. Significance Statement The global seafloor is made up of topography on scales ranging from centimeters to thousands of kilometers. Exactly how sloping bottoms on the scale of hundreds of kilometers affect wave energization and propagation, and turbulence, is still poorly understood. Here, we investigate how topography affects geophysical flows in various stages of the energy cycle, such as stable wave modes, unstable wave modes, and turbulent flow, using an idealized two-layer representation of a large patch of the ocean. The role of topography is shown to be highly dependent upon the bottom slope magnitude and sign. These results have implications for the fundamental understanding of geophysical fluid mechanics and how to represent topographic effects in the ocean components of relatively coarse climate models.