Using Hydraulic Theory to Monitor Dense Overflows in a Parabolic Channel


Deep ocean passages are advantageous sites for long term monitoring of deep transport and other physical properties relevant to climate. Rotating hydraulic theory provides potential for simplifying monitoring strategy by reducing the number of quantities that need to be measured. However, the applicability of these theories has been limited by idealizations such as restriction to zero or uniform potential vorticity ( pv ) and to channels with rectangular cross sections. Here the relationship between the flow characteristics in a canonical sea-strait and its upstream condition is studied using uniform pv rotating hydraulic theory and a reduced-gravity shallow-water numerical model that allows for variation in pv . The paper is focused mainly on the sensitivity of the hydraulic solution to the strait geometry. We study the dynamics of channels with continuously varying (parabolic) cross-sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. The results showthat far enough from the channel entrance, the hydraulically controlled flowin the strait is insensitive to the basin circulation regardless of parabolic curvature. The controlled transport relation is derived for the case of uniform pv theory. Comparing the model to theory, we find that the measurement of the wetted edges of the interface height at the critical section can be used to estimate the volume flux. Based on this finding, we suggest three monitoring strategies for transport estimation and compare the estimates with the observed values at the Faroe Bank Channel. The results showed that the estimated transports are within the range of observed values.