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Consider an isothermal atmosphere at rest. (a) Using hydrostatic balance, show that pressure p and potential temperature are respectively given by and 0 Ooe²/Hs H₂ = P = Poe-²/H where the isothermal and isentropic scale heights are given by H H₁ = cpTo/g and To is the temperature. How is o related to po and To? = RTo/g and

Consider an isothermal atmosphere at rest. (a) Using hydrostatic balance, show that pressure p and potential temperature are respectively given by and 0 Ooe²/Hs H₂ = P = Poe-²/H where the isothermal and isentropic scale heights are given by H H₁ = cpTo/g and To is the temperature. How is o related to po and To? = RTo/g and

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
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Consider an isothermal atmosphere at rest. (a) Using hydrostatic balance, show that pressure p and potential temperature are respectively given by P = Poe and 0 = 0²/Hs RTo/g and where the isothermal and isentropic scale heights are given by H = cpTo/g and To is the temperature. How is o related to po and To? (b) Show that the Brunt-Vaisala frequency squared N² = g/H、 for an isothermal H₂ atmosphere. = -z/H (c) Calculate H, H, and N for To = 250K.
Transcribed Image Text:Consider an isothermal atmosphere at rest. (a) Using hydrostatic balance, show that pressure p and potential temperature are respectively given by P = Poe and 0 = 0²/Hs RTo/g and where the isothermal and isentropic scale heights are given by H = cpTo/g and To is the temperature. How is o related to po and To? (b) Show that the Brunt-Vaisala frequency squared N² = g/H、 for an isothermal H₂ atmosphere. = -z/H (c) Calculate H, H, and N for To = 250K.
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