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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 ∂ ∂ ∂ ∂ ∂ ∂ = ∂ ∂ => = ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = 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, one likes to use potential temperature instead of temperature in the thermodynamic equation. Why? 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 1 = 1 1 1 41 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 ∂ ∂ ∂ ∂ = ∂ ∂ θ θ θ p w s V t ∂ ∂ ∂ ∂ = ∂ ∂ θ θ θ s n V Considering only the horizontal advection, the equations become s θ V t θ ∂ ∂ = ∂ ∂ 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 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 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 Δ 2 ) , , Δ ( ) , , Δ + ( Δ ) , , ( = ) Δ + , , ( θ θ θ θ Temperature Advection using the forward in time and centered difference in 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 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 time and upstream method in space . In using the equation in the ....
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This note was uploaded on 10/08/2010 for the course GEOG 1172 taught by Professor Snyder during the Summer '10 term at Minnesota Colleges.
 Summer '10
 snyder

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