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(a) show that the horizontal momentum equation without friction can be written as dv/dt = −fk × v where f is the Coriolis parameter, and k is the vertical component of Earth's angular velocity and v ≡ u − ug is the velocity deviation with respect to the geostrophic velocity. (b) show that this equation leads to d2v/dt2 + f2v = 0 , (2) (c) What type of motion does this equation represent? What is the period of oscillation?

(a) show that the horizontal momentum equation without friction can be written as dv/dt = −fk × v where f is the Coriolis parameter, and k is the vertical component of Earth's angular velocity and v ≡ u − ug is the velocity deviation with respect to the geostrophic velocity. (b) show that this equation leads to d2v/dt2 + f2v = 0 , (2) (c) What type of motion does this equation represent? What is the period of oscillation?

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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Let us show that the geostrophic balance is stable and, when perturbed, leads to oscillatory motion (referred to as inertial oscillations). For this purpose,
(a) show that the horizontal momentum equation without friction can be written as


dv/dt = −fk × v

where f is the Coriolis parameter, and k is the vertical component of Earth's angular velocity and v ≡ u − ug is the velocity deviation with respect to the geostrophic velocity.


(b) show that this equation leads to


d2v/dt2 + f2v = 0 , (2)


(c) What type of motion does this equation represent? What is the period of oscillation?

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