Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow

Abstract

The analysis of two-layer exchange flow through contractions with a barotropic component treated by Armi & Farmer (1986) is extended to include exchange flows over sills and through a combination of a sill and contraction. It is shown that exchange over a sill is fundamentally different from exchange through a contraction. Control at the sill crest acts primarily through the deeper layer into which the sill projects and only indirectly controls the surface layer. This asymmetry in the control results in asymmetrical flows. The interface depth above the crest is not one half the total depth, as assumed in other studies by analogy with flow through contractions, but is somewhat deeper; the maximal exchange rate is less than for flow through a contraction of equal depth. When both a sill and a contraction are present, the contraction influences control at the sill crest only if it lies between the sill and the source of denser water. The response to barotropic flow is also asymmetrical: the transition to single-layer flow occurs at much lower speeds for a barotropic component in one direction than the other.Results of the analysis are applied to exchange flow through the Strait of Gibraltar, which includes both a sill and a contraction. It is shown that maximal exchange conditions apply throughout part of the tidal cycle, and observations illustrate several of the analytical predictions for barotropic flows, including the formation of fronts, single-layer flow, submaximal exchange and reverse flow.

Role of mixing in the structure and evolution of a buoyant discharge plume

“…The nature of this lift-off, and the role of mixing in the near field are two key components of understanding near field structure. Observations of river plumes have found that lift-off typically occurs uniformly across the cross section [e.g., Wright and Coleman, 1971], consistent with two-layer hydraulic theory [i.e., Armi and Farmer, 1986;Farmer and Armi, 1986], or at an angle to the cross section, consistent with a two-dimensional (2-D) extension of hydraulic theory [MacDonald and Geyer, 2005]. Landward of the lift-off location, the discharging water mass is essentially unmodified, but substantial mixing occurs seaward of the lift-off in both the Mississippi [Wright and Coleman, 1971] and Fraser River [MacDonald and Geyer, 2004] outflows.…”

“…This will happen when either the lateral encroachment of the plume by colder ambient waters at depth overcomes vertical mixing processes and closes in across the entire plume, or when the local bathymetry triggers the formation of a bottom front. Liftoff in the latter case can be well described by classic one dimensional two-layer hydraulic theory [e.g., Armi and Farmer, 1986;Farmer and Armi, 1986], or more recent two-dimensional extensions of hydraulic theory [MacDonald and Geyer, 2005], which are beyond the scope of the present study. Atkinson [1993] and others have predicted lift off points for a uniformly sloping bottom.…”

Surface Imprints of Water-Column Turbulence: A Case Study of Tidal Flow over an Estuarine Sill

“…In situ measurements reported by Baschek et al [13,14] have elucidated various physical processes active near the sill on flood tide ( Figure 2). Guided by internal hydraulic theory [15,16], Baschek et al [13] divide the flow response into two distinct stages of forcing: "strong" and "extreme".…”

“…Internal waves believed to originate at the Boundary Pass sill have been observed in Georgia Strait [22,23], but in the far-field, well downstream of the region shown in Figure 2. Also, during "intermediate" tidal forcing [15,17], buoyant surface water can occur upstream of the sill [14], so that the flow response may include upstream effects such as internal jumps and solibores [19,20] (Representative temperature and salinity profiles at Boundary Pass can be found in reference [24]). …”

Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation

“…In the past few years, several time-dependant two-layer numerical models (Liu et al, 2015;Ljubenkov, 2015;Sierra et al, 2004) were developed to describe the two-layer flow in salt-wedge estuaries. Although the main features of the stratified flow were captured by these models, they are not shock-capturing, and thus cannot correctly describe the internally transcritical flow which may occur under highly dynamical conditions due to sills or lateral contractions (Armi, 1986, Farmer andArmi, 1986).…”