Working Up Hills: Dynamics over Sloping Topography with Bottom-Enhanced Diffusion
Creators: Diehl, Benjamin William
Publisher: name: Columbia University
Year: 2012
Subjects: subject: Mathematics
subject: FOS: Mathematics

description: The deep ocean circulation is known to have influence even at the surface, through means such as the Meridional Overturning Circulation (MOC).  Initial theories on abyssal circulation and mixing have been improving, based on observation of both physical and numerical experiments.  By tracing this progression, key aspects are identified but the explanations and relationships between them still contain gaps.  Vertical diffusivity is one such component known to influence the strength of the MOC and is a part of the least understood leg of that circulation.  Observations in particular have identified intense regions of mixing occurring near, and likely caused by, rough topography.  Though the pieces are all present from this brief description, the exact relationships between them are still unclear, and observations cannot fully be generalized without more direct knowledge of how the phenomena interact. With these issues in mind, two models were used for simulating two dimensional abyssal canyons having constant sloping topography and bottom-intensified mixing acting on an initial uniform stratification.  The first model uses finite volumes on a uniform z-coordinate grid, and it was set up and used to verify general sensitivity and confirm the choice of experimental variables while keeping the rest constant in a base state.  The second model, developed specifically for use in this investigation, employed finite element techniques with a nonuniform mesh.  A variational problem was created from derived streamfunction-vorticity equations plus advection-diffusion of a sole tracer, potential temperature.  Preliminary simulations confirmed that both models were capable of simulating the desired phenomena, notably an upslope flow along the topography, and had otherwise comparable results. Two diagnostics were used for analyzing both models: the minimum value of streamfunction is a proxy for flux of a bottom boundary layer, and an estimate of thickness for the bottommost layer is a minimum length of communication into the fluid interior.  These two diagnostics were studied in relation to changes in the amount of bottom enhanced mixing and also to changes in slope angle of the underlying topography.  The boundary layer thickness increases with slope angle, a trend thought to continue well beyond tested values.  Likewise, the streamfunction minima closely follow a linear relationship determined by the maximum diffusivity.  Additionally, the variability within the values for both diagnostics are seen to decrease in response to either diffusivity decreases or slope length increases.  Tangent investigations focusing on slope length and effects of periodic domains add support to the results as well as demonstrate potential robustness of the identified trends.  With this restriction in mind, all slopes (0.0025-0.0075) and diffusivities (0.05-0.3 m2/s) generate intense layers over 100m high with over 0.1Sv of up-slope flow, comparable to that observed in along-canyon flows.