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

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.

Seasonal Change of the Mixed Layer Structure at Tsukuba

“…In Fig. 2 Gamo et al (1983), the relationships between MMD, H0, and the potential temperature profile which consists of n stable layers are as follows :…”

“…3, fair weather days with light winds are mainly grouped into the above three types. Other fair weather types are shown in Gamo (1983).…”

On the Vertical Diffusion from a Ground Level Source in the Atmospheric Boundary Layer

“…The relation between the heat flux and the insolation has not been given theoretically yet. Empirically, Gamo et al (1976) found that qo is approximately 40% of the insolation. Therefore, we assume qo=0.4 I.…”

“…Recently, on the basis of airplane observations performed by Gamo et al (1976), Yokoyama et al (1977a, b, c) proposed a structure model of the turbulence in the atmospheric boundary layer. This model was later examined by Gamo and Yokoyama (1979) in the mixing layer and Yamamoto et al (1979) in the stable layer and appeared to be reasonable for most boundary layers except extremely stable layers. In the extremely stable layer, they suggested that more careful observation be conducted to develop the structure model.…”

“…Above the surface layer or in the upper convective layer, Yokoyama et al (1977a) proposed the eddy diffusivity in the form and where C1' is a universal constant and *(*) is a nondimensional universal function of *. According to the observations by Gamo et al (1976),…”