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Abstract

The transient double-diffusive stability problem for a horizontal layer of salty water bounded by two rigid isothermal surfaces was examined using both the frozen-time technique leading to an eigenvalue problem and the linear amplification theory leading to an initial value problem. Initially, the layer was subjected to zero temperature and salinity gradients. At the time t = 0, uniform step increases in both temperature and salinity were imposed at the bottom surface while the top surface is impermeable to the diffusion of salt. In the early developing stages scaling lengths based on thermal and mass boundary layer thicknesses were taken into consideration. Several parameters were considered in the analysis, namely, the thermal and solute Grashof numbers, Prandtl number, Schmidt number, time and wave size. Stability results based on the frozen-time technique and the linear amplification theory were compared in order to check the validity of the frozen-time technique within the range of the system parameters considered.

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Transient Double-Diffusive Salinity in a Horizontal Fluid Layer

Abstract

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