The dynamics of rotating two-layer exchange flows : an analytical and numerical modelling study

Abstract

Two-layer hydraulic exchange flows with zero potential vorticity and zero net flux are modelled analytically for rectangular channels with a constriction, a sill and a combination of the two. Controlled flows are determined for a range of non-dimensional channel widths L, scaled by the Rossby radius, and Bernoulli potentials ΔE; and these are traced along the channels. The interface between the two layers is linear and may separate from either side wall of the channel, all possible flow regimes are considered when tracing the solutions.

The flows are traced using a method analogue to the Froude number plane developed by Armi (1986), for channels with L ∝ √D, where D is the non dimensional channel depth. Flow along other geometries is traced using the Gill functional approach (Gill, 1977). Maximal and submaximal flows are derived and discussed for a variety of channel geometries.

Analogous to the non-rotating case, most flows through a flat bottom channel are traceable. Flow through a channel with a sill is traceable only for a limited range of Bernoulli potentials, which depend on the width of the channel at the control. It is shown that the virtual control of a maximal flow over a sill does not need to coincide with the entrance of the channel, as has been assumed in most previous studies of hydraulically controlled flows over a sill. The controlled fluxes are derived for a comprehensive range of Bernoulli potentials as well as channel widths L. A method for determining the long wave-speeds in the channel is outlined.

In the second part of this thesis two-layer exchange flows are modelled numerically using MICOM (Miami Isopycnic Coordinate Ocean Model) in an idealised set up with two rectangular basins separated by a rectangular channel with a sill. A comprehensive set of 71 experiments is run varying the rotation rate f, the density difference between the two layers Δρ, and the interface level in the dense reservoir, ΔH.

The flow features in the top and bottom layer are described for two experiments and compared to the theoretical results in the thesis, as well as observations and laboratory experiments. The typical 'crossing-over' of the bottom layer at the top of the sill is found and a boundary current forms on the left-hand side looking upstream. The majority of the transport in the top layer is confined to a boundary current on the left-hand side of the channel, a feature that has never been described before, but which is also predicted by the theory. It is shown that all flows exhibit inherent time variability, which is disregarded in the steady hydraulic theory.

The flux results confirm that as rotation and therefore L, increases the non-dimensional flux reaches a maximum, and so rotation imposes an upper limit on the flow. An empirical parameterisation for two-layer exchange flows is derived using the MICOM results. The transport across the sill is found to depend on ΔH.^3/2 a result expected for non-rotating flows, but that does not derive from the scaling of the rotating theory.

Idealised models of the Faroe-Bank-Channel and the Denmark Strait are run and transport results are compared to observations in these straits. The Denmark Strait is only poorly modelled by a two-layer exchange while agreements for the Faroe-Bank-Channel is somewhat better.

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