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48 3 Basics of Geophysical Fluid DynamicsAt location X = x = 0 and Y = y = 5 km, a disturbance is introduced such thatthe flui parcel obtains a relative speed of u o = 0.5 m/s and v o = 0.5 m/s. In the f xedcoordinate frame, the initial velocity is U o = 0.864 m/s and V o =0.5m/s.The results show that the resultant path of the flui parcel is elliptical (Fig. 3.16).With a closer inspection of selected snapshots of the animation (Fig. 3.17), we canalso see that the flui parcel comes closest to the rim of the tank twice duringone full revolution of the flui tank. This finding which is simply the result ofthe elliptical path, is the important clue to understand why so-called inertial oscillations,described below, have periods half that associated with the rotating coordinatesystem.Fig. 3.16 Trajectory of motion (white line) for one complete revolution of a clockwise rotatingflui tank as seen in the f xed frame of reference. The SciLab script “Traject” in the folder “Miscellaneous/CoriolisForce” of the CD-ROM produces an animationFig. 3.17 Same as Fig. 3.16, but shown for different time instances of the simulation. The tankrotates in a clockwise sense. The star denotes a f xed location at the rim of the rotation tank3.12.7 Numerical CodeIn finite-di ference form, the momentum equations (3.37) can be written as:U n+1 = U n − Δt · Ω 2 X n and V n+1 = V n − Δt · Ω 2 Y n (3.40)