Abstract
AbstractIt is our aim with this paper to investigate how the presence of a continental shelf and slope alters the relationship between interior ocean dynamics and western boundary (coastal) sea level. The assumption of a flat-bottomed basin with vertical sidewall at the coast is shown to hide the role that depth plays in the net force acting on the coast. A linear β-plane theory is then developed describing the transmission of sea level over variable depth bathymetry as analogous to the steady advection–diffusion of a thermal fluid. The parameter , relating the friction parameter r to the bathymetry depth H and width , is found to determine the contribution of interior sea level to coastal sea level, with small giving maximum penetration and large maximum insulation. In the small (infinite friction) limit the frictional boundary layer extends far offshore, and coastal sea level tends toward the vertical sidewall solution. Adding simple stratification produces exactly the same result but with reduced effective depth and hence enhanced penetration. Penetration can be further enhanced by permitting weakly nonlinear variations of thermocline depth. Wider and shallower shelves relative to the overall scales are also shown to maximize penetration for realistic values of . The theory implies that resolution of bathymetry and representation of friction can have a large impact on simulated coastal sea level, calling into question the ability of coarse-resolution models to accurately represent processes determining the dynamic coastal sea level.
Highlights
Improvements in geoid determination enabled Woodworth et al (2012), Higginson et al (2015), and Lin et al (2015) to demonstrate that sea level (SL) along coastal boundaries can differ markedly from the adjacent open ocean
Note that we have found a simpler way to derive the Minobe et al (2017) result, this relies on certain assumptions about interior ocean dynamics, for example, that there is no interaction with bathymetry within the basin to disturb Sverdrup balance and that there is no outflow along the northern boundary, which would imply a nonzero zonal integral of meridional velocity in Eq (2)
We have shown that the assumption of a vertical sidewall at the coast within a western boundary allows coastal SL to be independent of layer thickness and the friction parameter and that the vertical sidewall solution is a special limit case for the more general problem that includes sloping bathymetry
Summary
Improvements in geoid determination enabled Woodworth et al (2012), Higginson et al (2015), and Lin et al (2015) to demonstrate that sea level (SL) along coastal boundaries can differ markedly from the adjacent open ocean (interior). For basins modeled with flat bottoms and vertical sidewalls, Stommel (1948) showed that a solution for the circulation could be found by balancing the vorticity added by wind stress with bottom friction This approach resulted in boundary layers running north– south, which Munk (1950) further developed by replacing bottom friction with lateral friction, a more realistic assumption for flows that do not reach the bottom. For the case of modeling large-scale SL along western boundaries, allowing the Coriolis parameter to change and maintaining consistency when applying the boundary condition with the deep ocean are, as will be seen, crucial This added complexity has contributed to limiting the study of SL in western boundary regions over sloping bathymetry.
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