Buoyancy force reversals in vertical natural convection flows in cold water

Abstract

Calculated numerical results are presented for laminar buoyancy-induced flows driven by thermal transport to or from a vertical isothermal surface in cold pure and saline water wherein a density extremum arises. The present calculations specifically explore the consequences of temperature conditions wherein the buoyancy force reverses across the thermal region owing to the presence of a density extremum within the region. Such conditions commonly occur in terrestrial waters and in technological processes utilizing cold water. The linear approximation of density dependence on temperature, used in conventional analysis, is here replaced by a very accurate non-linear density equation of state for both pure and saline water. This permits an accurate treatment of such flows for bounding temperatures up to 20 °C at ambient salinity and pressure levels from 0 to 40 p.p.t. and 1 to 1000 bars, respectively. The results may be applied to the melting or slow freezing of a vertical ice surface in pure water as well as to a heated or cooled vertical isothermal surface in pure or saline water. For example, buoyancy force reversals arise for a vertical ice surface at 0 °C melting in fresh water between 4 °C and 8 °C at atmospheric pressure. Temperature conditions for which buoyancy force reversals occur are of special interest because of the resulting anomalous flow behaviour and low surface heat-transfer rates. The transition from conditions with no buoyancy-force reversal to those resulting in a large buoyancy-force reversal is accompanied by as much as 50% decrease in surface heat transfer. This produces a corresponding trend in the melt rate of a vertical ice surface in pure water. Sufficiently strong buoyancy force reversals are found to cause local flow reversal either at the edge of the flow layer or near the surface. Conditions are determined for which flow reversals occur at each of these locations. These local flow reversals are the precursors of convective inversion, that is, of the reversal of the net flow direction with changing ambient medium temperature. Limits on conditions for convective inversion are determined. Calculated transport is compared with previous experimental results, with good agreement throughout the several regions of such complicated flows. The calculations indicate that such flows are relatively very weak. However, their form may lead to early laminar instability.