Laserfiche WebLink
<br />18 <br /> <br />of cloudy air above the updraft maximum where UR > 0 does not, on the other <br /> <br />hand, affect the average per unit mass value of the cloud parameters. Sil1ce the <br /> <br />mass of detrained cloudy air is very much less than the mass of environmental air <br /> <br />with which it mixes, the dilution of the environment is insignificant and it is <br /> <br />assumed that the values of the environmental parameters are unchanged by the de- <br /> <br />trainment process. <br /> <br />Mass Continuity Equation <br /> <br />Since the model cloud is one-dimensional in the vertical and has only impl icit <br /> <br />horizontal motion terms, the system of dynamic equations can be closed by specifying <br /> <br />the radial advective velocity UR as that velocity (as a function of time and height) <br /> <br /> <br />which will maintain mass continuity when inserted in the vertical velocity equation. <br /> <br />The mass continuity equation can be written in the form: <br /> <br />2URR = _ 1. OP _ W ~ _ ~ <br />p at p clZ &7Z <br /> <br />(eq. 15) <br /> <br />it can be shown that: <br /> <br />c)P_ <br />it - 0 <br /> <br />(eq. 16) <br /> <br />p = 2506.612 pO .714/91 <br /> <br />(eq. 17) <br /> <br />SI = (1 +0.61 q) <br /> <br />(eq. 18) <br /> <br />which upon substitution yields <br /> <br />2 UR 1 as 0.61 ~q W ap ~W <br />-rr-=e ~+ 1+0.61qclt - pn-rr <br /> <br />(eq. 19) <br /> <br />'"'", <br />