申論題

3. Applications (30 points)

(c) Let's flip the dimension to x-z plane and remove the moving plate so that the upper boundary is now free surface (Fig. 1b). Wind forcing is applied at the free surface. Assuming that the wind-driven flow is steady, laminar, two dimensional, and fully developed in x direction (ie. no gradients in x). The flow is subject to the tollowing boundary conditions: (1) at z = 0, u = v=w = 0. (2) at z = H, the viscous stress (τ) is only non-zero in x direction, with
Express the momentum balance and solve for the velocity profile (u(z) ) (9 points)