Pages 129-134
The numerical model of mixing in stratified flows developed in the previous paper was extended to the unstable condition of the mixing by surface cooling. The use of the relative variation of density to the initial density difference as one of principle variables accures accurate representation of small variation of density due to temperature change. The transport equation of this quantity together with the incompressible Navier-Stokes equation for an inhomogeneous fluid is solved by the finite volume method. The surface cooling with the constant temperature on the top is modeled as the Dirichlet boundary condition for the transport equation. The two-dimensional computation was carried out to examine the mixing process in an infinitely large area of temperature stratification by surface cooling. Vertical profile of horizontally averaged temperature shows the interface separating the mixed layer from the stratified region. It is confirmed that the rate at which the interface descends depends upon the ratio of the temperature difference due to the surface cooling to that due to the stratification. The roll structure extended to the whole depth of the mixed layer is found to be fundamental to the mixing process in the two-dimensional flow. At an early stage the structure consists of a row of rolls with opposite rotation alternately aligned with the top surface and it is still maintained even in the following chaotic circumstance of the growth and merging of rolls where some distinct blobs penetrate the mixed layer.
