Basedon the obtainedrelations, one is able to find that the width of the salt fingers
is proportional to the length of the salt fingers in 1/4 power (scaling relation that was
conrmedin numerous experiments).
L h1=4 : (2.22)
Relying on the above formula, Stern calculated the typical width of the “salt fingers”
andcomparedit with the experimental data obtainedby Stommel et al. [1]. Stern found
that the width was about 0.2–0:3 cm, very close to the experimental value of the width
0:3 cm.
The planar form of the “salt fingers” cells (a top view) was observedand investigated
qualitatively in the first experimental work of Stommel et al. [1] in 1968.
It was discovered that in the salt–temperature double-diffusive system, the planar
form of these cells is polygon-like (mainly rectangular or square forms) and the typical
width of the “salt finger” cells is about 0.3–0:6 cm.
Shirtclife and Turner [5] carried out more detailed quantitative experiments in which
the morphology of the “salt fingers” cells was investigatedby means of optical methods.
It was conrmed that the “salt fingers” have mainly square plane form and the cells
oriented both parallel as well as orthogonal to the beaker walls (a rectangular beaker
was used). Shirtclife and Turner noted that the cells rotated very slowly around their
main axes (for each cell, there is a main axis, which is parallel to the z-axis and
passing through the center of the cell).
A more detaile dandcomprehensive analysis of “salt fingers” regime was performed
by Baines and Gill [6]. They drew the state diagram and calculated critical values of
the RT ; RS for “salt–temperature” and “salt–sugar” double-diffusive systems, for which
one can observe “salt fingers” phenomenon, but the mechanism of the “salt fingers”
instability was not proposed.
Stern was the first to give a theoretical explanation for the problem in 1967 [1,7],
when he wrote down the following condition for the “salt finger” instability:
FS
(@T=@z) ¿ const ≈ 1 : (2.23)
It follows from the expression that either too larger salinity (S component) Gux
of gradient of the salt concentration FS or too smaller temperature (T components)
gradient (@T=@z) leads to instability, while the internal gravity waves arise and destroy
the ends of columnar “salt nger” cells. Relying on this formula, one can explain why
the “salt fingers” are destroyed at their ends: the temperature gradients at the ends of
the “salt fingers” are too small to be compared with the temperature gradient at the
interface between the two layers.
Hence,
FS
(@T=@z) ¿ 1 (2.24)
is aroundunity andturbulence convection arises