lect_09 - Are All Of These Terms Important? du uv tan uw 1...

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1 Are All Of These Terms Important? rz ry rx F g u z p a v u dt dw F u y p a vw a u dt dv F w v x p a uw a uv dt du + Ω + = + + Ω = + + + Ω Ω + = + φ ρ cos 2 1 sin 2 1 tan cos 2 sin 2 1 tan 2 2 2 Scale Analysis • Goal: To determine relative importance of the terms in the basic equations for particular scales of motion. • Approach: Estimate the following quantities 1) The magnitude of the field variables. 2) The amplitudes of fluctuations in the field variables. (Used to estimate derivatives.) 3) The characteristic length, depth and time scales on which these flucutations occur.
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2 Scaling Quantities U = horizontal velocity scale W = vertical velocity scale L = length scale H = depth scale δ P = horizontal pressure fluctuation T = time scale (advective) = L/U P 0 = surface pressure scale Values of Scaling Quantities (midlatitude large-scale motions) 10 7 s 10 5 s T 10 7 Pa 10 5 Pa P 0 10 4 Pa 10 3 Pa δ P(hor izonta l) 10 3 m 10 4 m H 10 6 m 10 6 m L 10 -4 m s -1 10 -2 m s -1 W 10 -1 m s -1 10 m s -1 U Ocean Atmosphere Quantity
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3 Physical Constants 1 2 6 1 2 5 3 3 3 1 4 0 0 0 0 7 2 10 10 10 1 10 cos 2 sin 2 45 10 10 = = = = = Ω = Ω = = s m s m m kg m kg s f m a s m g o a o a ν ρ φ
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lect_09 - Are All Of These Terms Important? du uv tan uw 1...

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