A steady ocean current of uniform potential vorticity q = 5x107 m-s and volume flux Q = 4x10 m/s flows along isobaths of a uniformly sloping bottom(with bottom slope S = 1 m/km). Show that the velocity profile across the current is parabolic. What are the width of the current and the depth of the location of maximum velocity? Take f=7 x 105 s-.