The turbulence quantities such as the RMS of vertical wind speed *w, the dissipation rate of kinetic energy to heat *, and the vertical diffusion coefficient KM in the planetary boundary layer under near-neutral stability are considered. In this layer, observations have shown that *w is proportional to the friction velocity u* and decreases approximately linearly with height. Based upon these observations, u* is approximated by where u* is the friction velocity at height z, suffix 0 denotes the value at the surface and =1-z/h , h is the characteristic scale height relating to the thickness of the boundary layer. The turbulence quantities are related to u* by replacing u*0 in the relations given by the similarity theory attributed to Monin and Obukhov (1954), for the constant flux layer, these are as follows; where C with suffix w or KM is constant, k is * constant. The above relations hold fairly well with the observations taken in lower region of the boundary layer below the height of 700 to 1000m approximately.
In order to derive simple relations expressing the vertical profiles of turbulence quantities such as the rms values of vertical speed *w and temperature *T, the vertical diffusion coefficient for momentum KM, and the dissipation rate of kinetic energy * in the planetary boundary layer (PBL), the similarity hypothesis, which was attributed to Monin and Obukhov (1954) and verified in the constant flux layer (CFL), is extended. Unlike the CFL, the horizontally homogeneous PBL is, in general, non-stationary. However, here, approximately stationary conditions are dealt with by taking sampling times for the turbulence quantities which are relatively short when compared with the time change of the conditions. As in the case of the CFL, the fundamental quantities which determine the structure of the PBL are the vertical flux of sensible heat q, and momentum u*, and scale of turbulence l. However, in the PBL, these differ from their CFL behavior q and u* vary with height z, and l is not linearly proportional to z. In the present PBL model, the height variations of q, u*, and l are expressed by suitable empirical relations and the layer thickness is defined by the height at which the extrapolated values of q and u* tend to zero. The vertical profiles of the turbulence quantities in the PBL are derived by replacing q0, u*0, z (suffix o denotes surface value) in the relations for the CFL by q, u* and l. The derived relations are compared with observation and the characteristics of the scale l are considered.
To clarify the behavior of the standard deviation of vertical velocity *w under various meteorological conditions, many data obtained by tethered balloon, high tower and light airplane were analized. Relations between *w, wind speed U, and many meteorological elements, for example, insolation, local lapse rate, Pasquill's stability categories, classification of cloud and inversion base height, were checked. It has been found from observations at height of 50 m that *w was proportional to U in case of weak insolation while with increasing of insolation, * w tended to show characteristics caused by free convective fluctuations. Temperature gradient at the observation height of *w can not explain variation of the relation between *w and U with stability. Pasquill's stability categories are not explanatory index either for the *w-U relations, except at 50m. Three different relations between *w and U were found from observations taken at various heights. First is the relation for strong convective layer; second, in the layer below inversion base; and third, in the inversion layer. In the case of second group, there is a critical wind speed Uc*. When U is weaker than Uc*, free convection is predominant and *w is independent of wind speed. When U is stronger than Uc*, however, forced convection is predominant and * w/U tends to be constant. The height dependency of Uc* was observed.
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.
The turbulent structure under stable conditions in the atmospheric boundary layer (ABL) has been investigated by tower measurements, of the turbulent fluctuations and vertical mean profiles of wind velocity and air temperature. The results are summarized as follows: (1) For the parameter of thickness of the turbulent ABL under stable conditions, the height hq at which turbulent heat flux disappears is a more reasonable choice than the height h* derived from the potential temperature profile, and hq has linear relation to the Monin-Obukhov stability length. (2) Unlike the constant flux layer near the ground, the absolute values of vertical heat flux (q) and momentum flux (u*) decrease with height in the stable ABL. According to these results, the ABL model proposed by Yokoyama et al. (1977, 1979) is applied to the turbulent ABL under stable conditions. We conclude that the vertical profiles of q and u* are approximated by the power function *m and *n, respectively (where, * =1-z/h q, z: height, hq: thickness of the layer, m *3/2, n *1/2) and the same relations which described the turbulence quantities, temperature and wind velocity gradients in the constant flux layer are valid for whole stable ABL by replacing surface values of q and u* by their local values.
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