A laboratory and quantitative model of finite-amplitude thermohaline intrusions
DYNAMICS OF ATMOSPHERES AND OCEANS, 30 (2-4):
71--99 (1999)Abstract
An experiment that models the growth and evolution of double-diffusively
driven intrusions across an initially sharp thermohaline front is
described. A removable barrier was placed in the center of a 2 m
long tank that was stratified with equal density gradients of sugar
solution on the left and salt solution on the right. After the barrier
was removed and small lateral density differences had been adjusted,
an organized set of laterally intrusive layers formed. These consisted
of layers of fingers separated by diffusive interfaces sloping systematically
upwards from the high-S (sugar) side of the front. Each layer consisted
of a central, finger-filled region plus "nose" regions on either
side in which fingers do not extend through the complete layer depth.
The sugar concentration within the layers decreased smoothly from
the high-S side to the low-S and increased with height in the finger
region as required for the existence of sugar fingers. This structure
spread in a self-similar fashion as the layers extended into previously
undisturbed fluid. The lateral velocity within each intrusion was
Z-shaped, with nearly uniform vertical shear in the finger zones
and stronger shear of opposite sign across the diffusive interfaces.
The peak layer velocity increased from the nose extension velocity
U-n at the noses to about 3.7 U-n in the centre of the front. This
implies significant horizontal divergence and consequent vertical
motion and recirculation within the layers, with unknown effects
on the finger fluxes. The velocity structure, like the S, has spread
with the noses and the front in a self-similar manner. The nose velocity
was constant with time and proportional to the S-jump across the
front. Using the results of Ruddick and Turner (1979) Ruddick, B.,
Turner, J.S., 1979. The vertical length scale of double-diffusive
intrusions. Deep-Sea Res. 26A, 903-913 for the vertical scale of
the layers, the nose velocity was found to be approximately described
by a constant, but very small, Froude number of 0.005. The lateral
S-flux was measured directly (by re-inserting the barrier after some
time had elapsed) as well as from correlations between layer velocity
and S, and was well-described by assuming that the front spread with
the noses. The S-flux was therefore proportional to the nose velocity
times the lateral S-contrast, or alternatively, to the square of
the lateral S-contrast. This flux is independent of the frontal width.
The main structural features of the laboratory intrusions are consistent
with the assumption that the flow is in a state of continuous hydrostatic
adjustment close to equilibrium with the ambient stratified density
field. The depth difference between the two ends of the layers is
shown to be equal to the total layer thickness, and the length of
the nose beyond the finger-filled region on the more-diffusive side
is r(S) times the total length of the finger-filled region, where
rs is the ratio of the (top-to-bottom) to (end-Co-end) differences
in the layer of the less-diffusive solute. Consideration of the advective
fluxes provides another relation involving r(S), the (finger) flux
ratio gamma and density differences across the layer which leads
to an expression for the layer depth similar to that given by Ruddick
and Turner (1979) but with a little less empiricism. A salt balance
equating the flux across the vertical centerline to the rate of increase
of total salt content beyond it connects r(S) to the ratio of the
maximum velocity of the mean circulation to the rate of extension
of the nose, which was measured. This gives r(S) = 0.46 +/- 0.4 and
gamma = 0.67 +/- 0.03 for the flux ratio in these cells. A more complete
theory to account for the detailed circulation patterns and flow
speeds has not yet been developed. (C) 1999 Published by Elsevier
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