Journal of Fluid Mechanics



Ice blocks melting into a salinity gradient


Herbert E.  Huppert a1 and J. Stewart  Turner a2
a1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge
a2 Research School of Earth Sciences, Australian National University, Canberra

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huppert he   [Google Scholar] 
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Abstract

In our previous qualitative paper, it was shown that when a vertical ice surface melts into a stable salinity gradient, the melt water spreads out into the interior in a series of nearly horizontal layers. The experiments reported here are aimed at quantifying this effect, which could be of some importance in the application to melting icebergs. Experiments have also been carried out with heated and cooled vertical walls at larger Rayleigh numbers R than those of previous experiments.

The main result is that for most of our experiments there is no significant difference between these three cases when properly scaled. The layer thickness over a wide range of R is described to within the experimental accuracy by \[ h=0.65 [\rho(T_w,S_{\infty}) - \rho(T_{\infty},S_{\infty})]\left/\frac{d\rho}{dz}\right., \] where the term in brackets is the horizontal buoyancy difference evaluated at the mean salinity and dp/dz is the vertical density gradient due to salinity. In the case of ice melting into warm water the effective wall temperature Tw is approximately 0°C, whereas in colder water the freezing point depression must be taken explicitly into account. A detailed examination of the vertically flowing inner melt water layer in both homogeneous and salinity stratified cases has been made. This layer and the melt water which is mixed outwards from it into the turbulent horizontal layers have little effect on the outer flow. At high R and large external salinity, however, mixing can reduce the effective salinity at the inner edge of the horizontal layers, and thus the layer scale. A puzzling feature is the relatively weak dependence of layer scale on local salinity, though the vigour of convection and the rate of melting are greater where the salinity is high.

The direct application of our results to oceanographic situations predicts layer scales under typical summer conditions of order tens of metres in the Antarctic and of order metres in the Arctic. More measurements will be needed, especially close to icebergs, before the application of these ideas to polar regions can be properly evaluated.

(Published Online April 19 2006)
(Received June 21 1979)
(Revised November 21 1979)



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