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Cloud Microphysics simulation

######My attempt at creating a cloud microphysics simulation

This is intended to be a simulation of how water droplets form and get large enough to eventually fallout of clouds as rain.

Math Basis

The math basis for this program is the spontaneous condensation of cloud water droplets and the subsequent collision and coalescence of the droplets.

Math formula come from

Condensation Model

  • Page 99

Growth of condensed water droplets is given by:

r(t) = sqrt(r_o**2 + 2Et)

r_ o is original droplet size. E is a special parameter.

E = 1/(F_k + F+_d) ==> this value is dependent on pressure and temperature.

Can expand the above equations using the definitions F_k and F_d

F_k: Can be estimated as -1 to a good accuracy

F_d = (pR_vT)/(D*e_s(T))

p: density of water = 1000 [kg/m**3]

R_v: gas constant for water vapor = 461 [J K−1 kg−1]

T: Temperature = varies, [K]

D: Molecular Diffusion Coefficient: at T=0C: 2.06*10**-5 (m**2)/s

NOTE** D varies with temperature and would need a more accurate solution to calculate to a better approximation

e_s(T): saturated vapor pressure at temperature

Sufficient for drops larger than r = 10 µm

Role of Condensation Nuclei

  • Page 81-81

Collision Model

Condensation alone does not account for the presence of rain on the time scales typically observed. This is because around r = 20 µm, the collisions of the droplets become important.

The volume of a sphere is given by: V=(4/3)π(r^3)

When two spheres collide, the new radius is given by r = (r_1^3 + r_2^3)^1/3

This will be important when displaying the objects as 2D circles as the radius of the circles will note simply add together as may be assumed.

Falling Droplets

The falling of cloud droplets is governed by the radius of the drop and the strength of the updraft velocity. Given a radius, it should be simple issue of getting updraft and downdraft difference in order to calculate the movement.

For r < 40 um

u = K_1r**2 where K_1 = 1.19x10^-6 cm^-1s^-2

The radius has to be in 'cm' to use this

40um < r < 0.6mm

u = K_3*r where K_3 = 8x10^3 s^-1

One issues facing the model is a lack of horizontal motion. In a real cloud the droplets would be moving about, both in the vertical and horizontal directions due to mixing within the cloud. A slight random horizontal motion may be able to keep the system from achieving stead state due to lack of horizontal motion.

References

"A Short Course in Cloud Physics" 3rd edition by R. R. Rogers and M. K. Yau

#TODO

  • Get formula for all models
  • create section that tests math formula before implementing
  • How to create buttons, sliders, checkboxes and drop down menus
  • Fill out math section on README.md