Forced-dissipative two-layer quasi-geostrophic instability, waves, and turbulence over an aligned sloping bottom

We investigate two-layer quasi-geostrophic (QG) turbulence over a sloping bottom using linear wave mode theory, energy and time scale diagnostics, and potential vorticity (PV) flux spectra.We consider bottom slopes of varying sign and magnitude with the topographic PV gradient aligned with the PV gradient due to background vertical shear.We show that, outside of the tropics, the ocean's most energetic regions have aligned bottom slopes, and that the topographic PV gradient generally dominates over the planetary PV gradient.In the two-layer QG model, bottom slope effects are shown to be twofold: i) small-to-moderate bottom slopes support topographic wave energization, and ii) moderate-to-large bottom slopes support cascade arrest, jet formation, and surface-intensified baroclinic waves.Somewhat counterintuitively, larger bottom slopes support stronger topographic arrest of nonlinear energy but less energetic topographic waves.Flow over an aligned sloping bottom that supports topographic wave propagation in the same (opposite) direction of the background flow is prograde (retrograde).Retrograde jets act as waveguides, and are persistent and self-maintaining.Interjet momentum flux divergence is important for retrograde jet self maintenance due to topographic suppression of interjet buoyancy fluxes.Prograde jets merge and split in time and space, and act as transient waveguides.For a given bottom slope magnitude, prograde flows have smaller characteristic length scales than retrograde flows.This length scale asymmetry is explained by the Doppler shift of the topographic waves.These results inform both fundamental theory of baroclinic turbulence over a bottom slope and topography-aware parameterizations of ocean eddies.SIGNIFICANCE STATEMENT: The global sea floor is made up of topography with 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 waves and turbulence in various stages of the energy cycle, such as stable wave modes, unstable wave modes, and turbulent flow.The role of topography is shown to be highly dependent upon bottom slope magnitude and sign.These results have implications for fundamental understanding of geophysical fluid mechanics, and how to represent topographic effects in the ocean components of relatively coarse climate models.