The diurnal variation of the wind and temperature fields in the Ekman layer is studied by solving the equation of motion and of heat conduction. Eddy diffusivity is assumed to take the values which are evaluated by the extrapolated use of a modified KEYPS equation to the Ekman layer. With regard to the boundary conditions, the standard lapse-rate is assumed at the upper boundary and a constant temperature is assumed at the lower boundary which is set up in the soil. In this kind of study, hitherto, the constant flux layers near the surface are assumed in order to avoid a large amount of calculation, but in the present work, the original prognaustic equations of the whole layer are directly integrated by use of the matrix method for finite difference equations. Computation is carried out until cyclic solutions of one day period are obtained.The computed results are compared with observations available to us at present.
Assuming a steady and horizontal flow and thermal stratification in the Ekman layer, it is investigated how the wind structure in the layer is affected by thermal stratification. For this purpose an extrapolated application of the turbulent transfer relations, which hold in the lowest tens meters, to the entire layer is made. The wind and stress vectors and exchange coefficient are calculated numerically as functions of height, thermal stratification and roughness parameter. It is found that the shape of the Ekman spiral is affected by thermal stratification in such a way that the wind component normal to isobar increases generally with increase of stability. It is also found that the magnitude of the stress decreases with increase of stability, that the wind speed in the lower layer decreases with increase of stability, and that the height of the Ekman layer increases with increase of instability. Comparison of the calculated results with observed data is made on the surface values, indicating fairly good agreement._
Diffusion of particles having an equal fall velocity which are released from a crosswind line source in diabatic atmospheres is studied. The wind profile and eddy diffusivity assumed in this investigation are those proposed by Yamamoto and Shimanuki as a revision of the KEYPS formula. The solution of the resulting diffusion equation is obtained numerically for various combinations of the source height, thermal stability and terminal velocity of the particles. In addition the deposition rate of particles on the ground is estimated as a function of the downwind distance, source height and stability. Diffusion of particles having different sizes is then estimated. 1.
The equation of wind shear proposed by Yamamoto and Shimanuki which is a modified form of so-called KEYPS equation is solved approximately. The approximate formulae of wind shear are rational expressions of|| 1 /2 and ||13, where is defined by the ratio of height and stability length. Relative errors involved in the approximate formulae of wind shear, wind velocity and eddy diffusivity do not exceed 0.4 percent under unstable conditions and 0.6 percent under stable conditions. Function subprograms used for computing velocity and diffusivity by electronic computer are written by FORTRAN language.
Instantaneous images of the smoke released to the unstable surface boundary layer from a chimney are simulated numerically.The characteristic patterns of instantaneous images are formed by introducing spatial correlation of velocity. Trajectories correlated spatially are obtained by use of random variables correlated spatially in a Markov chain equation. In order to generate the field of random variables correlated spatially, a random number is given for each region divided by a length corresponding to the scale of turbulence.Empirical profiles of the mean and fluctuation of wind velocity are used in the Markov chain. The scale of turbulence is estimated from these profiles. Numerical simulations of the diffusion released from a source of 60 m height were carried out. Under certain atmospheric conditions, some samples of image are formed. The results with irregular patterns seem to be realistic. The spatial correlation of velocity was detected from the results of simulation, which is smaller than that of the given random variable.
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