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50 3 Basics of Geophysical Fluid DynamicsFig. 3.18 Pathway of an object that experiences the Coriolis force in a clockwise rotating f uid.The SciLab script “Coriolis Force Revealed.sce” in the folder “Miscellaneous/Coriolis Force” ofthe CD-ROM produces an animationcircle twice while the tank revolves only once about its centre. Accordingly, theperiod of this so-called inertial oscillation is 0.5 T , known as inertial period, withT being the rotation period of the flui tank.Rather than working in a fi ed coordinate system, it is more convenient to formulatethe Coriolis force from the viewpoint of an observer in the rotating frame ofreference. In the absence of other forces, it can be shown that inertial oscillationsare governed by the momentum equations:∂u∂t=+2Ω v and ∂v∂t=−2Ω u (3.47)The Coriolis force acts perpendicular to the direction of motion and the factorof 2 reflect the fact that inertial oscillations have a period half that of the rotatingframe of reference. If a parcel is pushed with an initial speed of u o into a certaindirection, it can also be shown that its resultant path is a circle of radius u o /(2 |Ω)|).With an initial speed of about 0.7 m/s and |Ω| = 0.727×10 −5 s −1 , as in the aboveexample, this inertial radius is about 4.8 km.3.13 The Coriolis Force on Earth3.13.1 The Local VerticalIn rotating fluid at rest, the centrifugal force is compensated by pressure-gradientforces associated with slight modificatio of the shape of the flui surface. On therotating Earth, this leads to a minor variation of the gravity force by less than 0.4%.The local vertical at any geographical location is now define as the coordinateaxis aligned at right angle to the equilibrium sea surface. This implies that, for a