3) Kelvin's circulation theorem. Kelvin's circulation theorem is invoked in studying meteorology. The theorem involves t

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3 Kelvin S Circulation Theorem Kelvin S Circulation Theorem Is Invoked In Studying Meteorology The Theorem Involves T 1 (121.83 KiB) Viewed 115 times

3) Kelvin's circulation theorem. Kelvin's circulation theorem is invoked in studying meteorology. The theorem involves the equation Dr = f dr + pū & Dū Ddr Dt (1) Dt Dt where D/Dt is some material derivative operator, r is a circulation around a material contour, and ū is the velocity of a barotropic ideal fluid. (A barotropic fluid means that its density depends only on pressure.) a) Given that Dū/Dt = - Õp/p + žo, where p is the density of the fluid, p is the pressure, and o is some scalar potential, evaluate the first term in the right-hand side of Equation (1). Reminder: Please provide a step-by-step and clear solution. b) Furthermore, given that DdF/Dt = (di . 7)ā, evaluate the second term in the right-hand side of Equation (1). Reminder: Please provide a step-by-step and clear solution. c) Finally, using your results in a) and b), what is the numerical value of Dr/Dt in Equation (1)? What is its physical interpretation? =