The momentum equations for a rotating shallow homogeneous fluid with a free upper surface (i.e. the shallow water equations) may be written as Əh Du Dt Dv Dt = +fv-g Əh ду = -fu-g- (1) where u(x, y, t), v(x, y, t) are the velocities on the free surface, and h(x, y, t) is the depth of the free surface. (a) Rewrite (1) and (2) by expanding the total derivative operator D Ə Ә Ə +u- +v Dt Ət əx ду du = (5 + 1) = − (5 + 1) (² Dt (2) (b) Use the two equations you developed in Part(a) to derive the evolution equation for $+f, where = Qu. In other words, show that dy Əv + əx ду (3) being careful to explain the steps. [Hint: start by deriving the equation for and then use the fact that the Coriolis parameter f = f(y) only.]

The momentum equations for a rotating shallow homogeneous fluid with a free upper surface (i.e. the shallow water equations) may be written as Əh Du Dt Dv Dt = +fv-g Əh ду = -fu-g- (1) where u(x, y, t), v(x, y, t) are the velocities on the free surface, and h(x, y, t) is the depth of the free surface. (a) Rewrite (1) and (2) by expanding the total derivative operator D Ə Ә Ə +u- +v Dt Ət əx ду du = (5 + 1) = − (5 + 1) (² Dt (2) (b) Use the two equations you developed in Part(a) to derive the evolution equation for $+f, where = Qu. In other words, show that dy Əv + əx ду (3) being careful to explain the steps. [Hint: start by deriving the equation for and then use the fact that the Coriolis parameter f = f(y) only.]

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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