Fog Formula III

In Zakharova (1972) [1] there is the BOUNDARY CONDITIONS section from pages 9 to 12. There is outlined the mathematics for the initial and boundary conditions for the evolution of radiation fog. Jennings (2024, 2025) [2, 3] presents Zakharova’s mathematics on fog and in this paper, the author goes further to delve into the math of fog. For z –> zo (zo is a parameter of roughness), u –> 0 and v –> 0. Also, the flow of turbulent kinetic energy is absent, as ∂ b2 / ∂ z –> 0. At z = 0 (the ground) there is no water content and the specific humidity at all moments of time remains constant. The underlying surface absorbs the fog droplets, so N (t, 0) = 0. N is presented in equation (16a) in Jennings (2025) and is the total number of droplets in 1 cm3 of cloudy air. Later, Zakharov goes to INITIAL CONDITIONS (t = 0) for u, v and b2. This will be developed here.