Growth of the Mixing Depth and the Diurnal Variation of Vertical Profiles of Temperature and Turbulence Characteristics in the Mixing Layer

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Abstract
A simple but practical model for the growth of a connective mixing layer is derived by integrating the entrainment rate equation proposed by Deardorff et al. (1969). The development of the mixing layer height is determined by three parameters which are the potential temperature gradient in the stable layer capping the mixing layer, integrated surface heat flux and initial value of the mixing depth. Also a model for the time-height variation of the turbulence structure in the mixing layer is proposed based on the above growth theory and turbulence structure model of the mixing layer presented by Yokoyama et al. (1977a). In this paper, the surface heat flux is assumed to be proportional to the insolation disregarding absorption by the atmosphere. The model is applied to data obtained by airplane over flat terrain in the vicinity of Tokyo, in March 1972, summarized by Gamo et al. (1976a). Estimation of the diurnal variation of the mixing layer structure including potential temperature, energy dissipation rate, rms of vertical wind fluctuations and turbulent eddy diffusivity seems to agree favorably with observations.