43i14 Ijaet0514287 V6 Iss2 945to953

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43i14 Ijaet0514287 V6 Iss2 945to953
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  International Journal of Advances in Engineering & Technology, May 2013.©IJAET ISSN: 2231-1963   945 Vol. 6, Issue 2, pp. 945-953 A   S TUDY ON E ARTH C LOUD S PACE I NFLUENCED BY C ERTAIN D YNAMICS F ACTORS   Vivekanand Yadav and R. S. Yadav   Department of Electronics and communication EngineeringJ K Institute for Applied Physics and TechnologyUniversity of Allahabad, Allahabad  –  211002 A BSTRACT     In this paper, dynamics factors and their influences in the formation of earth ’s cloud field have been studied.These influences are mainly based on heat and water-vapour flow equations in a turbulence atmosphere. Theequations for cloud water content have been developed, considering the influence of vertical movement and heat, cold advection and turbulence exchange. The conditions of formation and development of many form of cloud are observed in mesospheric region. I.   I NTRODUCTION   The clouds are formed a result of the transformation of water vapour form a gaseous into a liquid or solid state. The optical properties of clouds differ from the properties of a cloudless atmosphere. Therelationships between atmospheric (air) temperature T   and clouds exceed many times the relationships between T and greenhouse gases and admixtures, primarily carbon dioxide Matveev.et.al [1]. Theformation of cyclones (including tropical ones), tornados, strong winds, and floods is closely relatedto clouds Steven M. Smith [13], Matveev.et.al [9-10], Michael A.Persinger [11]   and Stubenrauch.t.al[12].Matveev.et.al [2  –  4] obtained formulas for changes in air temperature and cloud water content withtime under the action of vertical movement. In this paper, other factors have been investigated whichinfluence the formation and development of a cloud depending on the atmospheric temperature andwater content. The accuracy of the results of this paper is obtained by the help of MATLABSimulation setup.The paper has been devided into sections: Initial Equations, Vertical Movement,   Turbulence,   CloudFormation and the Change in Water Content with Time, results and discussions, conclusion and futurework. II.   I NITIAL E QUATIONS   Before any cloud forms, water vapor must achieve a state of saturation and the relative air humiditymust attain a value of f =   –  100%. Since the pressure of saturated water vapor E is a function of temperature, to estimate change f, it is necessary to use the flow (balance) equation for water vapor and the heat flow (balance) equation.We write the heat balance equation in the form        L    =  (1)Where T and P are air temperature and Pressure; R is the gas constant;   is the heat capacity of air; Lis the heat of vapor transformation (condensation);  =         is the operator of the total (individual)derivative; u, v and w are the airspeed(wind speed) projectionsalong axes x, y and z(axis z is directed upward along the vertical0; t is time ; and   is the turbulentflow of heat(all quantity refer to 1kg of air).  International Journal of Advances in Engineering & Technology, May 2013.©IJAET ISSN: 2231-1963   946 Vol. 6, Issue 2, pp. 945-953 The mass fraction of saturated water vapour    entering into the third summand in the left-hand sideof (1) is related to the saturation pressure () by the correlation.   =0 .622E (T)/p (2)Logarithmically differentiating it, we obtain the balance equation for water vapor in a saturated state(in a cloud):By (2)Log   = log ( 0 .622) +log E (T)  –  log pDifferentiating w. r. t, t, we have      = 0+  () ()        =  (  () ()   ) +   (3)  =      (4)Where   = 4.  is the gas constant for water vapour.By (1)   =  -L [{   (  () ()   )} +   ] +   , by (3)   =    +    -    () () -   +       =  + . () - L . ()     -   +   by (4)   =  + .()    –     .()        –    +     [   .()    ]    = (   .()  )       –    +       [1 .()      ]    =   ( RTp+L 0.622E(T) )       –    +       [1 .()      ]    = R  (1+ .()R )       –    +      =      (+ .() )(+ .() )    (  –  )(+ .() )    =       (  –  )(+ .() )   (5)   Where a = (+ .() )(+ .() ) (6)By (3),    =  (  () ()   ) +    By (4),  =       Putting the value of   in (3), we have  International Journal of Advances in Engineering & Technology, May 2013.©IJAET ISSN: 2231-1963   947 Vol. 6, Issue 2, pp. 945-953    =  [     (       (  –  )(+ .() ) )  ) +   ]    =  {          +   (  –  )(+ .() )    )  }+        =     {  (       -1)    +   (  –  )(+ .() )    }+       t = q m { R ( RR v c  R  R ) t +   (  –  )(+ .() )    } +       t = q mR (         -  ) t +     (  –  )(+ .() )    +       t = .R (         -  ) t   + .  (  –  )(+ .() )    +   from (2)   t = .R (   −R v c  R      )   t  .  (  –  )(+ .() )    +   (7)By (6)(1-a) = 1  –    +./+.  /        (1  –  a) = . (R−    )(      +.  )          (8)a = (R+.)(      + .  )        a = (R+.)(      + .  )     (9)Putting the value of  ‘ a ’ in (7), we have   t = .R ( (.)( .)   −R v c  R      )   t  .  (  –  )(+ .() )    +       t = .R ( −    (      + .  ) )   t  .  (  –  )(+ .() )    +       t = R. ( −    (      + .  ) )   t  .  (  –  )(+ .() )    +       t = R (1-a)   t  .  (  –  )(+ .() )    +   (10)a = (+ .() )(+ .() )  International Journal of Advances in Engineering & Technology, May 2013.©IJAET ISSN: 2231-1963   948 Vol. 6, Issue 2, pp. 945-953 a =     (11)Where   is moist-adiabatic gradient and   is dry- adiabatic gradient. Since   is always lessthan   , in moist-saturated (cloud) air, parameter a is always less than unity (a <1) . t <0 in case of a particle of air moving toward lower pressure. By (5) and (10), t <0 and δ  t <0 ,In saturated air, q m decreases then cloud water content  increasesThe increments of water content d  and temperature dT   as pressure changes are, according to (5) and(10), related by the correlations   t = R (1-a)   t (10a)  =    (5a)By eqs (10a) and (5a), we have dq m =  (1)aL   dq m =d , d=      (−)  (12)By equation (11), it is clear that for  dp<0   dT<0 and d>0 ,Also, when dq m < 0Then d>0.  Thus, the increment d in large cyclone is significant in our study.For case of unsaturated (dry air) L = 0, then (1) becomes       =  then (6) and (11) takethe form;a=1;     =1Then equation (10) becomes   t = .  (  –  )(+ .() )    +    Along the vertical, the correlation  =          (13)Becomes  =      =g (Static equation -  = g )    = g    where =  is the air density; g is the increase in the speed of freefallFrom (5) and (13), we have  =     ( g  ) +   (  –  )(+ .() )          = −  +   (  –  )(+ .() )    International Journal of Advances in Engineering & Technology, May 2013.©IJAET ISSN: 2231-1963   949 Vol. 6, Issue 2, pp. 945-953  = −     –  (       ) +   (  –  )(+ .() )    = −     –  {     ()} +   (  –  )(+ .() )   (=, .)    =(   ) - (     ) +   (  –  )(+ .() ) ( a =     )    =(       ) - (     ) +   (  –  )(+ .() ) (14)From (10) and (13), we have                = R (1-     ) (g  ) .  (  –  )(+ .() )    +                    =   (1-     )  .  (  –  )(+ .() )    +        =[   (    )    ]  –  (         ) + .  (  –  )(+ .() )    +     ( 15)   III.   V ERTICAL M OVEMENT (C ONVECTION ) From (3)    =  (  () ()   ) (16)E depends only on temperature and from (4),    =        = (  )  = -      (17)By Static equation (-  = g  )  = -     ( =  , R=    ) (18)By eqs. (17) and (18), eq. (16) becomes,    =  (-           ) (19)By eqs. (15) and (19), (    )  =[   (    )    ] (    )  = [  1         ] (    )  = [  1        (-           )] (19a)Advective heat and water-vapor flows, according to eqs. (14) and (15), are written in the form (  )  = - (     ) , (20) (    )  =  –  (         ) . (21)Logarithmically differentiating eq. (2) by x, we obtain
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