Bottom Friction in a Baroclinic Ocean: Influences on Sea Level and Slope Currents

In the flat-bottomed open ocean, the seawater density distribution yields alone the existence of geostrophic baroclinic currents and steric sea-level spatial changes. However, at basin margins, the bathymetry exerts a considerable control on both these quantities. Indeed, the steric sea level vanishes at the coast where depth is zero. Also, continental slopes are vorticity barriers hindering convergence (divergence) of baroclinic transport toward the coast and accumulation (removal) of water there. In the limit of no temporal development, how the coastal sea level is impacted by open-ocean density changes is hence nontrivial and must involve ageostrophic mechanisms. Here, we focus on bottom friction as one such process, provide derivations extending the arrested topographic wave theories to a fully baroclinic ocean, and discuss an application for an eastern boundary margin (representative of the Rockall Slope Current region, for example). We demonstrate that open-ocean density changes yield important joint effect of baroclinicity and relief (JEBAR) along-slope currents, which generate cross-slope Ekman currents due to friction with the seabed. The latter are associated with divergence and convergence leading to sea-level changes above the slope, mediated to the coast via coastally trapped waves. Through this process, not only the coastal sea level is modified but also the along-slope currents are slowed down to well-known asymptotical solutions. Hence, our results link modern theoretical developments in sea-level research and past analytical studies of slope currents. Our effort describes the fundamental notions, and we anticipate it paves the way for more sophisticated works.