Matrix Analysis of Parabolic Partial Differential Equation

It is studied how the size distribution of the so-called giant aerosols is changed by the diffusion-sedimentation and washout in the atmospheric boundary layer. An instantaneous and a continuous sources of infinite horizontal extent are assumed for ejection of aerosols into the atmosphere.The size distribution are calculated numerically as a function of time and height above ground for various combinations cf the eddy diffusivity profile and the rainfall intensity. The computational results are as follows. (1) The size distribution changes with time or height in such a way that the concentration of particles decreases with increase of particle size. (2) The effect of the diffusion-sedimentation simply reflects on the deformation of the size distribution of larger particles. (3) The degree of deformation of the size distribution by the washout increases with increase of particle size in the case of instantaneous source, and it is most pronounced for intermediate particle size range when the time duration of particle emission is sufficiently long.

“…(1) A computational method of the diffusion equation such as Eq. (1) with R = 0 was proposed by Shimanuki (1969). This method can also be applied to Eq.…”

Section: Appendixmentioning

confidence: 99%

Effect of Diffusion-Sedimentation and Washout Processes on Aerosol Size Distributions

Sato¹

1979

“…Since the condition for computational stability requires a time step smaller than 0.01 sec, it is not economical to carry out computation directly step by step. Therefore we shall adopt the matrix method proposed by Shimanuki (1969), available under the condition that *i+1,j or *i+1,j(j=1, 2,...n) is a linear combination of *i,j or *i,j (i,j=1,2...n), or all the elements of *ij and *ij are constants. If the eddy diffusivity and solar radiation are constants, and the approximation (29) is valid, then *ij and *ij become constants for all values of i and j.…”

Section: It Is Given Bymentioning

confidence: 99%

“…For large *, we can calculate A* and B* speedily, by converting * to a binomial form (see Shimanuki, 1969). Generally we calculate A* and B* for * =2* (* and * are integers).…”

Section: It Is Given Bymentioning

confidence: 99%

Diurnal Variation of Wind and Temperature Fields in the Ekman Layer

Yamamoto

Shimanuki

Aida

et al. 1973

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.

“…In order to solve Eq. 16 This condition is satisfied for a large downwind distance by using a large value of M. The finite difference equation 17was calculated by the matrix method proposed by Shimanuki (1969a). The matrix method is stated as follows : Eq.…”

Section: Ii) Boundary Conditionsmentioning

confidence: 99%

Diffusion of Falling Particles in Diabatic Atmospheres

Yamamoto

Shimanuki

Nishinomiya

1970

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.