Mixing in ocean straits and overflows

Tjipto J. Prastowo 1 , Ross W. Griffiths 1 , Graham O. Hughes 1 , Andrew McC. Hogg 1

1 Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia

We have measured the amount of mixing that occurs when two fluids of different density exchange in opposite directions through a constriction or over a sill. Such exchange flows commonly occur through ocean straits and over bottom sills. The constrictions control the rate of transport of water into or out of estuaries and marginal seas and between abyssal ocean basins. Analytical methods are frequently used to estimate exchange flows through these constrictions; we have focused on extending the simple analytical solutions to more realistic cases. Exchange flows involve strong velocity and density gradients between the two layers flowing in different directions, and this flow can become ‘critical' (i.e. reach the speed of gravity waves on the density interface) so that there is a hydraulic control point in the strait or above the sill.

We have observed that mixing occurs readily between the two layers by shear instability (figure 6; figure 7). The mixing produces a large volume of water having mixed properties, and it also modifies the mass flux through the constriction. This year we have examined in a series of experiments the role of the constriction geometry. The results have been included in a paper (Prastowo et al . 2006) that concentrates on the amount of mixing and the effect of the mixing on the exchange rates through a horizontal constriction. We find that mixing in the flow reduces the exchange rate by approximately 16% relative to that predicted by inviscid hydraulic theory, and that sidewall friction leads to a further reduction. The reduction increases with constriction length and decreases with minimum constriction width. The mixing can be described in terms of a efficiency – the proportion of the available potential energy (released by the flow over a given time) that is used to raise the centre of mass by vertical mixing. We find that the mixing efficiency depends only upon a Reynolds number based on the constriction length (figure 8). For Reynolds numbers in excess of 5 x 10 4 the efficiency takes a constant value of 11±1%. These measurements are in agreement with our previously developed scaling theories that predict both the observed exchange rate and the measured mixing efficiency. We have also completed this year a series of closely related experiments on exchange flows over sills. Ongoing work is now concentrating on interpreting the data and applying our theories to these cases.

 

Figure 6. Shear instability and mixing in an hydraulically-controlled exchange flow through a short constriction.

Figure 7. Shear instability and mixing in an hydraulically-controlled exchange flow through a long constriction.

Figure 8. The mixing efficiency (the proportion of potential energy released that goes into raising the centre of mass through mixing) computed from measurements of density profiles after the flow has proceeded for a given time.

References: Prastowo, T. J., Griffiths, R. W., Hughes, G. O. and Hogg, A. McC. (2006) Mixing due to exchange flows through a horizontal constriction. J. Fluid Mech ., submitted.