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For the case of a thunderstorm (convective scale) at 45°N latitude: a. Using the characteristic magnitudes below, perform a scale analysis for each of the three equations of motion (du/dt, dv/dt, dw/dt). U = 10 m/s L= 10 km = 104 m W = 10 m/s 1 mb ap (horizontal) = 100 Pa ap (vertical) = 1000 | L/U = 10³ s fo = 104 s¹ a = 107 m mb = 105 Pa = 10-5 S-1 v = 10-5 m² s-1 H = 10 km = 104 m b. What terms are important (i.e., large magnitude) in the equations? c. Recall that the Rossby number (Ro) is the ratio of the acceleration and Coriolis terms: Calculate the Rossby number for the system. U Ro= foL d. Should geostrophic balance be assumed for this system?

For the case of a thunderstorm (convective scale) at 45°N latitude: a. Using the characteristic magnitudes below, perform a scale analysis for each of the three equations of motion (du/dt, dv/dt, dw/dt). U = 10 m/s L= 10 km = 104 m W = 10 m/s 1 mb ap (horizontal) = 100 Pa ap (vertical) = 1000 | L/U = 10³ s fo = 104 s¹ a = 107 m mb = 105 Pa = 10-5 S-1 v = 10-5 m² s-1 H = 10 km = 104 m b. What terms are important (i.e., large magnitude) in the equations? c. Recall that the Rossby number (Ro) is the ratio of the acceleration and Coriolis terms: Calculate the Rossby number for the system. U Ro= foL d. Should geostrophic balance be assumed for this system?

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
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1. For the case of a thunderstorm (convective scale) at 45°N latitude: a. Using the characteristic magnitudes below, perform a scale analysis for each of the three equations of motion (du/dt, dv/dt, dw/dt). U = 10 m/s L = 10 km = 104 m W = 10 m/s ap (horizontal) = 1 mb = 100 Pa ap (vertical) = 1000 | L/U = 10³ s fo = 104 s-1 a = 107 m mb = 105 Pa Ω = 105 5-1 v = 10-5 m² s-1 H = 10 km = 104 m b. What terms are important (i.e., large magnitude) in the equations? c. Recall that the Rossby number (Ro) is the ratio of the acceleration and Coriolis terms: U Ro = foL Calculate the Rossby number for the system. d. Should geostrophic balance be assumed for this system?
Transcribed Image Text:1. For the case of a thunderstorm (convective scale) at 45°N latitude: a. Using the characteristic magnitudes below, perform a scale analysis for each of the three equations of motion (du/dt, dv/dt, dw/dt). U = 10 m/s L = 10 km = 104 m W = 10 m/s ap (horizontal) = 1 mb = 100 Pa ap (vertical) = 1000 | L/U = 10³ s fo = 104 s-1 a = 107 m mb = 105 Pa Ω = 105 5-1 v = 10-5 m² s-1 H = 10 km = 104 m b. What terms are important (i.e., large magnitude) in the equations? c. Recall that the Rossby number (Ro) is the ratio of the acceleration and Coriolis terms: U Ro = foL Calculate the Rossby number for the system. d. Should geostrophic balance be assumed for this system?
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