# Steady state Vertical diffusion equation

Hallo everyone,

I am trying to find the way to solve the vertical diffusion equation for a spicies X in the atmosphere for steady state conditions (dc/dt=0).

The equation has the form,

dJ/dz -P+S=0

where J =(vs*C(z)) + rho*kz*d/dz(C(z)/rho(z)) is the flux of spicies X at height z above ground level and C is the concentration of the spicies X at height z.

P = (lambda+sigma)*C(z) is the loss of X per unit time and per volume with the unit base
area and height dz at the altitude z.

S = source term of X
vs = gravitational sedimentory velocity
rho = air density
kz = turbulant diffusion coefficient

The boundary conditions that apply are

1) at altitude z= zn
lambda*C(zn)=q*S(zn) (equilibrium between formation and decay of X)

2) J (z=0) = 0

(Basically spices X is formed at z=31 Km and distributed or diffused in the atmosphere given by the equation above)

Help is greatly appricieted!!

Thanks

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Chestermiller
Mentor
Hallo everyone,

I am trying to find the way to solve the vertical diffusion equation for a spicies X in the atmosphere for steady state conditions (dc/dt=0).

The equation has the form,

dJ/dz -P+S=0

where J =(vs*C(z)) + rho*kz*d/dz(C(z)/rho(z)) is the flux of spicies X at height z above ground level and C is the concentration of the spicies X at height z.

P = (lambda+sigma)*C(z) is the loss of X per unit time and per volume with the unit base
area and height dz at the altitude z.

S = source term of X
vs = gravitational sedimentory velocity
rho = air density
kz = turbulant diffusion coefficient

The boundary conditions that apply are

1) at altitude z= zn
lambda*C(zn)=q*S(zn) (equilibrium between formation and decay of X)

2) J (z=0) = 0

(Basically spices X is formed at z=31 Km and distributed or diffused in the atmosphere given by the equation above)

Help is greatly appricieted!!

Thanks
See Miller, C., Meakin, P., Franks, R.G.E., and Jesson, J.P., The Fluorocarbon-Ozone Theory – V. One Dimensional Modeling of the Atmosphere: The Base Case, Atmospheric Environment, 12, 2481-2500 (1978)