Lec11_T_advection - Temperature Advection ...

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Unformatted text preview: Temperature Advection          advection e temperatur Potential z w- y v- x u- t z w y v x u t dt d = => = + + + = s) coordinate t p, y, x, (in p- y v- x u- t or advection e temperatur Potential = For a dry adiabatic process, In general, one likes to use potential temperature instead of temperature in the thermodynamic equation. Why? Temperature Advection [ ] ) , , ( ) , , + (- = - x z y x- z y x x u x u A B C x 10 o C 15 o C 20 o C 100km 100km Warm or cold temperature advection? m K s 000 , 100 5 m 1- = 1- 1- 1- 4-1 4 1 = 10 5 = 10 5 = h K .8- s K 1h 3600s- s K--- Temperature Advection In nature coordinates, these equations are written as: or , z w- s V- t = p w- s V- t = s n V Considering only the horizontal advection, the equations become s V t - = Similar to the previous example for the pressure gradient calculation, we need to compute only one advection term if we use the natural coordinates and make the s direction along the wind direction. x s 15 20 25 s n x s + s s - s Temperature Advection V ) , , ( t n s- s ) , , + ( t n s s ) , , ( t n s The finite difference form to compute the advection term can be written as: s t n s- s- t n s s t V- t n s t t n s 2 ) , , ( ) , , + ( ) , , ( = ) + , , ( Temperature Advection using the forward in time and centered difference in space , or s n x s + s s - s V ) , , ( t n s- s ) , , + ( t n s s ) , , ( t n s ) , , ( t n s ) , , + ( t n s s ) , , ( t n s- s s ) t , n , s s ( ) t , n , s ( t V ) t , n , s ( ) t t , n , s ( --- = + using the forward in time and upstream method in space . In using the equation in the ....
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Lec11_T_advection - Temperature Advection ...

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