The shallow water momentum equations in the Cartesian coordinate are (see (1.1.15) = = .yyyxt xxyxt Fgfuvvvuv Fgfvuvuuu a) Show the divergence equation can be derived as yyxxyyxxyyyxt FF vu gfvfufvu = ) 2 )(()]()([)()( 22 (hint: similar to the derivation of the vorticity equation section 1.4, rewrite the u, v equations as xxt FBvfu = )( yyt FBufv = )( but then to derive the equation for divergence, instead of vorticity) b) Linearize the divergence equation above and the vorticity equation (1.4.1), assuming the mean state is at rest )0,0,0(),,( = vu . c) Discuss the differences between the linearized divergence equation and vorticity equation. (For simplicity, you can even assume no rotation f =0 and no external forcing xF = yF =0!)