Sub-Maximal Exchange Flow over a Sill with Barotropic Forcing




Clouston, Ryan

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Two basins separated by a strait often have different densities due to environmental factors, resulting in a situation in the strait where fluids of different densities are essentially side-by-side, causing an exchange flow due to gravitational forces. Dense fluid is pulled below light fluid and the light fluid is pushed above the dense, creating an opposing flow in the two layers. This exchange is often “controlled” at the point in the strait where cross-sectional area is minimized due to a constriction, either horizontal or vertical. Exchange in the strait can control the dynamics, and in turn energy, nutrient, pollutant and biological transport between the basins. Since strait dynamics are often not resolved in regional or global models, it is useful to parameterize the exchange based on external variables such as the density difference in the basins, the level of the dense water in the dense basin, and the tidal forcing. Exchange flow can be “maximal” or “sub-maximal”. The flow is “maximal” if raising the interface in the dense basin (presumably by modifying light water to be dense) does not further increase the exchange flow through the strait. While many ocean straits are usually “maximal”, there are also many that are “sub-maximal,” and thus require separate theoretical treatment. Time-dependent external barotropic forcing (i.e. the tide) modifies the time-averaged exchange flow in a strait. The relationship between tidal forcing and the average exchange flow in a channel has been examined for maximal exchange (Helfrich, 1995). In the present study, that effort is extended to include tidal forcing on a sub-maximal exchange flow. A strait with a sill is simulated numerically, using a two layer hydrostatic approximation. Time-averaged exchange flow increases with tidal amplitude depending on three factors: the physical dimensions of the problem, the tidal amplitude, and the relative strength of flow of the density layers. Results show that all exchange flows increase at a similar rate with tidal forcing, after being normalized by a parameter relating physical dimensions of the strait to the interfacial wave speed. This result quantifies the exchange increase due to tidal forcing for all degrees of “maximality” in this simple sill-only geometry. This relates time-dependent sub-maximal flows to the maximal case that has already been studied in depth.



Sub-Maximal, Exchange, Maximal, Exchange Flow, Sill, Barotropic