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# Lec11_T_advection - I n ge ral onelike to usepote ne s...

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Temperature Advection advection e temperatur Potential z w - y v - x u - t z w y v x u t dt d = => 0 = + + + = θ θ θ θ θ θ θ θ θ s) coordinate t p, y, x, (in p - y v - x u - t or advection e temperatur Potential = θ ω θ θ θ For a dry adiabatic process, In general, onelikes to usepotential temperatureinstead of temperaturein the thermodynamic equation. Why?

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Temperature Advection [ ] ) , , ( ) , , Δ + ( - = - x z y x - z y x x u x u θ θ θ 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 0 1 - = 1 - 1 - 1 - 4 -1 4 1 = × 10 × 5 = 10 × 5 = h K .8 - s K 1h 3600s - s K - - -
Temperature Advection In naturecoordinates, theseequations arewritten as: or , z w - s V - t = θ θ θ p w - s V - t = θ θ θ s n V

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Considering only thehorizontal advection, theequations become s θ V t θ - = Similar to theprevious examplefor thepressuregradient calculation, weneed to computeonly oneadvection termif weusethenatural coordinates and makethes direction along thewind direction. x s Δ 15 20 25 s n x s + s s - s Temperature Advection V ) , , Δ ( t n s - s θ ) , , Δ + ( t n s s θ ) , , ( t n s θ
Thefinitedifferenceformto computetheadvection term can bewritten as: s t n s - s - t n s s t V - t n s t t n s Δ 2 ) , , Δ ( ) , , Δ + ( Δ ) , , ( = ) Δ + , , ( θ θ θ θ Temperature Advection using theforward in timeand centered differencein space , or s n x s + s s - s V ) , , Δ ( t n s - s θ ) , , Δ + ( t n s s θ ) , , ( t n s θ ) , , ( t n s θ ) , , Δ + ( t n s s θ ) , , Δ ( t n s - s θ

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s ) t , n , s s ( θ ) t , n , s ( θ t V ) t , n , s ( θ ) t t , n , s ( θ Δ Δ Δ Δ - - - = + using the forward in timeand upstreammethod in space . In using theequation in the naturecoordinates , wemay find it advantageous to choose s as thedistanceacross two isotherms. That will predeterminethevalueof θ ( s,n,t) - θ (s -∆ s,n,t) and all we haveto do is to measurethedistanceof s.
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