The momentum equations for a rotating shallow homogeneous fluid with a free upper surface (i.e. the shallow water equations) may be written as Du Əh (1) Dt +fv-9ax Əh Du = -fu- gay (2) Dt where u, v are the velocities on the free surface, and h is the depth of the free surface. (a) Rewrite (1) and (2) by expanding the total derivative operator ə D Ә ə = +u+v Dt Ət dz dy (b) Use the two equations you derived in Part(a) to derive the evolution equation for S+f, where =-. In other words, show that D 1/1₁ (5 + ƒ) = − (5 + ƒ) ( Dt Əu Əv + Әх 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 term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condit…