Onset of Convection in a Horizontal Layer of Cold Water

Abstract

Parabolic, cubic, and higher order expressions have been used in previous investigations to relate temperature to density in the vicinity of the density extremum. Another equation of state, based on the careful measurement of the density variations of both pure and saline water, has been used here to determine the onset of convection in a horizontally confined layer of water near its density extremum. The simplicity of this equation gives rise to a minimum number of problem particular parameters, and relatively easily allows for the inclusion of both pressure and salinity level effects (neglecting saline diffusion). The boundaries are considered to be rigid-rigid and of infinite thermal capacity. Present numerical results are compared with those previously calculated using other density relationships, including that embodied in the linear Oberbeck-Boussinesq approximation. Density extremum effects are seen to be stabilizing, with critical Rayleigh numbers calculated to be about 10 percent below those obtained using a parabolic density-temperature relationship and quite close to those found using a fifth-order polynomial. There is an associated increase in calculated wave number with the inclusion of density extremum effects.