A note on the transport across a diffusive interface

-The ratio of the fluxes of heat and salt across a diffusive interface is investigated on the premise that there are two contributions to the flux of each component. These contributions arise from the two transport mechanisms which can operate at a diffusive interface, viz. double-diffusive convection and turbulent entrainment. Estimates of the fluxes are provided for each process, and their combined effects are examined and compared with the experimental results of TURNER (1965) made in a heat-salt system. It is found that, by simply adding these two contributions, it is possible to explain the observed changeover from the constant regime to the variable regime which is in satisfactory agreement with the data. An estimate is also given for a sugar-salt system which is consistent with the, as yet semi-quantitative, observations. It is shown that turbulent mixing is only important in the variable regime, and in these circumstances, large fluxes of a component will be observed. THE DISCOVERY of temperature and salinity microstructure indicating the presence of interfaces separating a series of convecting layers (e.g. TAIT and HowE, 1968, DEGreeS and Ross, 1969) has led to an interest in the coupled vertical transports of heat and salt in such circumstances. As a result, the fluxes of heat and salt have been measured across both 'diffusive' and 'finger' interfaces (TURNER, 1965, 1967; CRAPPm% 1973; LINDEN, 1971, 1973a) formed between two layers by double-diffusive convection (see TtrRN~, 1973, Ch. 8). Of particular interest here are the laboratory measurements of the fluxes made across a diffusive interface, which are described briefly below. TURNER (1965) and CR~Pm~ (1973)t have measured the fluxes of heat F r and salt Fs across a diffusive interface, and related their data to the difference in temperature zJT and salinity AS between the layers. In ease of a diffusive interface, the lower layer is both warmer and saltier than the upper layer but is more dense: i.e. Rp -: [3/IS/o.AT ~ I, where a and fl are the proportional density changes for a unit change in temperature and salinity, respectively, and A denotes the magnitude of the change across the interface. They found that the measured ratio of the fluxes R! = [3Fs/aFT was related to Rp by a relationship of the form