A model of internal boundary-layer development

A slab model of the boundary layer was used to study the dynamics of the internal boundary layer associated with changes in surface temperature. The usual numerical procedure involving finite differences was avoided by solving the governing equations in a Lagrangian framework. The results of the modelling study showed that mixed-layer growth was enhanced by: (a) an increase in surface roughness; (b) an increase in the surface temperature change; and (c) a decrease in the horizontal velocity. It was found that the vertical velocity induced by variations in the horizontal velocity could play an important role in controlling the expansion of the mixed layer.The second part of the study involved the formulation of a model by simplifying the governing equations. The analytical solution obtained from the model compared favourably with the results of the numerical model. Furthermore, the analytical expression for the mixed-layer height was virtually identical to that presented by Raynor et al. (1974) to fit their observational data.