In this thesis I address several topics concerning the interaction of convection and density stratification in oceans and lakes. I present experimental and theoretical investigations of the
interaction between a localized buoyancy source and a heat flux through a horizontal boundary,
and of the interactions between salt fingers and intermittent turbulence or shear.
¶
An extensive series of laboratory experiments were used to quantify the stratification and circulation that result from the combined presence of a localized buoyancy source and a heat flux through a horizontal boundary. Previous studies found that convection in the form of a turbulent buoyant plume tends to produce a stable density stratification, whereas the distributed flux from a horizontal boundary tends to force vigorous overturning and to produce well-mixed layers. A new result of this thesis is that a steady density profile, consisting of a mixed layer and a stratified layer, can exist when the plume buoyancy flux is greater than the distributed flux. When the two fluxes originate from the same boundary, the steady state involves a balance between the rate at which the mixed layer deepens due to entrainment on the one hand and vertical advection of the stratified water far from the plume (due to the volume flux acquired by entrainment) on the other hand. There is a monotonic relationship between the normalized mixed layer depth and flux ratio R (boundary flux/plume flux) for 0 < R > 1, and the whole tank overturns for R > 1. The stable density gradient in the stratified region is primarily due to the buoyancy from the plume and for R > 0 there is a small increase in the gradient due to entrainment of buoyancy from the mixed layer. For the case of fluxes from a plume located at one boundary and a uniform heat flux from the opposite boundary the shape of the density
profile is that given by Baines & Turner (1969), with the gradient reduced by a factor (1 + R) due to the heating. Thus, when R < - 1 there is no stratified region and the whole water column
overturns. When 0 > R > - 1, the constant depth of the convecting layer is determined by the
Monin-Obukhov scale in the outflow from the plume.
¶
One application of these laboratory experiments is to surface cooling in lakes and reservoirs
that have shallow sidearms. During prolonged periods of atmospheric cooling, gravity currents can form in these sidearms and as the currents descend into the deeper waters they are analogous to isolated plumes. This can result in stratification at the base of a lake and an upwelling of cold water. Away from the shallow regions, surface cooling leads to a mixed surface layer. The depth of this layer will be steady when the rate of upwelling balances the rate at which the mixed layer deepens by turbulent entrainment. A series of laboratory experiments designed to model the depth distribution of a lake with a shallow sidearm showed that the steady depth of the mixed layer depended on the ratio of the area of the shallow region to the area of the deep region. Significant stratification resulted only when the reservoir had shallow regions that account for more than 50 % of the surface area. The depth of the surface mixed layer also depended on the ratio of the depths of the shallow and deep regions and no significant stratification forms if this ratio is greater than 0.5. These results are in good agreement with observations of circulation and stratification during long periods of winter cooling
from Chaffey reservoir, Australia. Theoretical time scales are also developed to predict the minimum duration of atmospheric cooling that can lead the development of stratification.
¶
In the second part of this thesis, I report a series of laboratory experiments which are designed to investigate the fine structure and buoyancy fluxes that result from salt finger convection in the presence of shear and intermittent turbulence. We find that, when salt finger convection in deep linear gradients is superposed with a depth-dependent spatially periodic shear, variations in the density profile develop on the same wavelength as the shear. The laboratory experiments presented in this thesis were carried out in a continuous density gradient with a spatially periodic shear produced by exciting a low-frequency baroclinic mode of vertical wavelength 60 mm. The density gradient consisted of opposing salt and sugar gradients favourable to salt fingers (an analogue to the oceanic heat/salt system). Where the shearing was large the salt finger buoyancy fluxes were small. Changes in salinity gradient due to the resulting flux divergence were self-amplifying until a steady state was reached in which the spatial variations in the ratio of salt and sugar gradients were such that the flux divergence vanished. Thus, along with reducing the mean salt finger buoyancy flux, a spatially varying shear can also lead to the formation of density structure.
¶
In the ocean intermittent turbulence can occur in isolated patches in salt finger-favourable
regions. I present new results from laboratory experiments in which a partially mixed patch
was produced in deep linear concentration gradients favourable to salt finger convection. Salt fingers give rise to an up gradient flux of buoyancy which can reduce the density gradient
in a partially mixed patch. This can then lead to overturning convection of the partially mixed
patch if a) the ratio of T and S gradients, R\rho =aTz/_ /betaSz, is near one, b) if turbulence results in
a nearly well-mixed patch and c) the patch thickness is large enough that convective eddies are
able to transport T and S faster than salt fingers. Once overturning occurs, subsequent turbulent
entrainment can lead to growth of the patch thickness. Experimental results agree well with
the theoretical prediction that h= \surd 8h B/N2 t, where h is the patch thickness, t is time, h is
the mixing efficiency of turbulent entrainment, B is the buoyancy flux of the salt fingers and N
is the buoyancy frequency of the ambient gradient region. This thickening is in contrast to the
collapse that a partially mixed patch would experience due to lateral intrusion in a very wide
tank. In regions of the ocean that contain salt fingers there is the possibility that, after a period
of initial collapse, an intrusion could enter a regime where the rate of collapse in the vertical is
balanced by the growth rate due to turbulent entrainment from the salt fingers buoyancy flux,
thus tending to maintain the rate of lateral spread.
¶
A further series of laboratory experiments quantified the buoyancy fluxes that result from
salt fingers and intermittent turbulence. A continuous density gradient, favourable to salt finger
convection, was stirred intermittently by an array of vertical rods that move horizontally back
and forth along the tank at a constant velocity. Previous experiments had found that continuous
turbulence destroys any salt fingers present because the dissipation of turbulent kinetic energy
occurs at scales that are generally smaller than salt fingers widths. However, when turbulence
is present only intermittently, the salt fingers may have time to grow between turbulent events
and so contribute to the vertical diffusivities of heat and salt. We conclude that the vertical
buoyancy flux of salt fingers is strongly dependent upon the intermittency of the turbulence,
and equilibrium fluxes are only achieved if the time between turbulent events is much greater
than the e-folding time of the salt fingers. When these results are applied to an oceanographic
setting, the effect of intermittent turbulence, occurring more 5% of the time, is to reduce the
effective eddy diffusivity due to salt fingers below equilibrium salt finger values, so that at
R\rho > > 2 the eddy diffusivity is due only to turbulence. The time averaged salt fingers fluxes are
not significantly reduced by intermittent turbulence when R\rho > 2 or if the intermittence occurs
less than 2% of the time, and so may contribute significant diapycnal fluxes in many parts of
the ocean.
| Identifer | oai:union.ndltd.org:ADTP/216707 |
| Date | January 2001 |
| Creators | Wells, Mathew Graeme, mathew@inferno.phys.tue.nl |
| Publisher | The Australian National University. Research School of Earth Sciences |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://www.anu.edu.au/legal/copyright/copyrit.html), Copyright Mathew Graeme Wells |
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