Assume we have a local coordinate system at latitude L on the earth’s surface with east, north, and up as the x, y, and z directions, respectively. In this coordinate system, the earth’s angular velocity vector is Ω = (0, ω cos L, ω sin L). Let w = (w₁,w₂, 0) be a wind vector.

(a) Determine the components of the Coriolis force vector F_c = −2mΩ × w.

(b) The equation −V∇p + F_c = 0 results from balancing the pressure gradient force, −V∇p, and the Coriolis force. Show that the x- and y-components of this equation result in Eq. 5.

Transcribed Image Text:

, V = 2mo(sin L)wz and V = -2mo(sin L)wi ax