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

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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 φ ρ φ φ φ ρ φ 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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