Diffusive boundary layers over varying topography

Abstract

Diffusive bottom boundary layers can produce upslope flows in a stratified fluid. Accumulating observations suggest that these boundary layers may drive upwelling and mixing in mid-ocean ridge flank canyons. However, most studies of diffusive bottom boundary layers to date have concentrated on constant bottom slopes. We present a study of how diffusive boundary layers interact with various idealized topography, such as changes in bottom slope, slopes with corrugations and isolated sills. We use linear theory and numerical simulations in the regional ocean modeling system (ROMS) model to show changes in bottom slope can cause convergences and divergences within the boundary layer, in turn causing fluid exchanges that reach far into the overlying fluid and alter stratification far from the bottom. We also identify several different regimes of boundary-layer behaviour for topography with oceanographically relevant size and shape, including reversing flows and overflows, and we develop a simple theory that predicts the regime boundaries, including what topographies will generate overflows. As observations also suggest there may be overflows in deep canyons where the flow passes over isolated bumps and sills, this parameter range may be particularly significant for understanding the role of boundary layers in the deep ocean.

Mixing-Driven Mean Flows and Submesoscale Eddies over Mid-Ocean Ridge Flanks and Fracture Zone Canyons

“…Can up-ridge mean flows within canyons be strong enough to maintain stratification without the need for restratification by submesoscale eddies? In calculations with uniform mixing and an infinitely deep rectangular canyon, Dell (2013) found mean flows parallel to the canyon axis that were indeed stronger than predicted by one-dimensional theory, but these flows were oriented largely along isopycnals and thus had little effect on the stratification. We here extend Dell's calculations to the more realistic case with bottomintensified mixing and a canyon that has sloping walls and is embedded in a ridge flank (Fig.…”

“…Boundary layer theory neglects any variations of the flow in the plane of the slope. Such variations can arise if the far-field stratification is not constant (e.g., Phillips et al 1986), if the mixing is inhomogeneous in the plane of the slope (e.g., McDougall 1989), and if there are variations in the slope itself (e.g., Dell and Pratt 2015;Holmes et al 2018). We here focus on the latter case, considering a full mid-ocean ridge (Fig.…”

“…In contrast to a uniform slope, the full ridge considered here has cross-ridge variations in the slope and thus allows for cross-ridge variations in the mixing-driven flow. Such variations can drive mass convergence or divergence and thus a so-called tertiary circulation (e.g., Garrett 1991;Dell and Pratt 2015;Holmes et al 2018). It is so far unclear whether this affects the mixing-layer stratification and its maintenance in the face of bottomintensified mixing, which will be the first topic investigated in this study.…”

Abyssal Circulation Driven by Near-Boundary Mixing: Water Mass Transformations and Interior Stratification

“…We emulate the PGCM solution by using finite differences to solve the time-dependent boundary layer equations (21)-(23) with the local Coriolis parameter f(y) and slope angle u(x, y) at each (x, y) cell of the PGCM grid, which is a sensible approach given that the parameters f(y) and u(x, y) vary on scales larger than the those of the boundary layer solutions (Dell and Pratt 2015). Since these local boundary layer solutions are given in terms of the local slope-normal direction z 0 rather than the true vertical direction z, we project the solution onto the true vertical direction z with the substitution z 0 / z/cosu and linearly interpolate from the projected z levels of the boundary layer solution to the PGCM's local s levels.…”

Low-Reynolds-number diffusion-driven flow around a horizontal cylinder

“…Phillips (1970) examined the importance of these flows to mass transport along a fissure in a geological context while Wunsch (1970) postulated that the boundary layers arising from the motion might play a role in oceanic mixing. More recently, Dell & Pratt (2015) suggested that it could drive upwelling near mid-ocean ridges.…”