3) Lets revisit the 2-D shallow water equations, but this time assume no rotation (f= 0)...

 

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3) Lets revisit the 2-D shallow water equations, but this time assume no rotation (f= 0) but the wave is embedded in a mean zonal flow U: V= (U+u'(x, 1)) + v'(x, 1); (1) where variables in bold are vectors. Under the approximation that fu'/U < < 1, if we can linearize our governing equations [see class notes equations (5.9) and (5.10)] to be and Ju' + Ot 9 A B C Ov' Iv' +U Ot Iv' Ot +U = H + (2) (3) (4) a) Describe in words: what are equation (2), (3) and (4)? Describe in words the meaning of each term A, B and C in equation 2. b) Now we will solve equations (2), (3) and (4). To simplify, lets first define the operator a P( ) = +U (5) Now rewrite the equations using this operator. To solve the equations, we want to reduce three equations with three variables, to one equation with one variable. The easiest way to do this is to operate on equation (4) with C and substitute in equations (2) and (3) to form one equation for n. Do it and show your work. 3) Lets revisit the 2-D shallow water equations, but this time assume no rotation (f= 0) but the wave is embedded in a mean zonal flow U: V= (U+u'(x, 1)) + v'(x, 1); (1) where variables in bold are vectors. Under the approximation that fu'/U < < 1, if we can linearize our governing equations [see class notes equations (5.9) and (5.10)] to be and Ju' + Ot 9 A B C Ov' Iv' +U Ot Iv' Ot +U = H + (2) (3) (4) a) Describe in words: what are equation (2), (3) and (4)? Describe in words the meaning of each term A, B and C in equation 2. b) Now we will solve equations (2), (3) and (4). To simplify, lets first define the operator a P( ) = +U (5) Now rewrite the equations using this operator. To solve the equations, we want to reduce three equations with three variables, to one equation with one variable. The easiest way to do this is to operate on equation (4) with C and substitute in equations (2) and (3) to form one equation for n. Do it and show your work.