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Unformatted text preview: Balanced Flow • The pressure and velocity distributions in atmospheric systems are related by relatively simple, approximate force balances. • We can gain a qualitative understanding by considering steady-state conditions , in which the fluid flow does not vary with time, and by assuming there are no vertical motions. • To explore these balanced flow conditions, it is useful to define a new coordinate system, known as natural coordinates. Natural Coordinates • Natural coordinates are defined by a set of mutually orthogonal unit vectors whose orientation depends on the direction of the flow. t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ Unit vector points along the direction of the flow. Unit vector is perpendicular to the flow, with positive to the left. Unit vector points upward. t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ t ˆ n ˆ k ˆ Horizontal velocity: t V V ˆ = r V is the horizontal speed, which is a nonnegative scalar defined by , dt ds V ≡ where is the curve followed by a fluid parcel moving in the horizontal plane. ( ) t y x s , , To determine acceleration following the fluid motion, ( ) dt t ˆ d V dt dV t ˆ dt V d t ˆ V dt d dt V d + = = r r t R δ t δψ n δ s t+ δ t δψ V R n dt ds ds t d dt t d R n ds t d R R R t t t R s ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ = = = < > = = = = δ δ δ δψ radius of curvature (positive in positive n direction) if air parcels turn toward left if air parcels turn toward right...
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This note was uploaded on 10/25/2011 for the course ENVSCI 324 taught by Professor Broccoli during the Spring '11 term at Rutgers.
- Spring '11