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56 3 Basics of Geophysical Fluid Dynamics3.14.7 Inertial OscillationsThe aim of this section is to predict the pathway of a non-buoyant parcel floatinwith an ambient uniform fl w (U o , V o ) subject to a series of abrupt wind events. Themomentum equations governing this problem can be formally written as:∂u∂t∂v∂t=+f v + ∂u f∂t=−fu+ ∂v f∂t(3.55)(3.56)where u f and v f are forcing terms assumed to be uniform in space. The pathway ofthe flui parcel can then be calculated from:dxdt= U o + u and dydt= V o + v (3.57)To illustrate this process, we consider an ambient fl w with velocity componentsof (U o , V o ) = (5 cm/s, 5 cm/s), corresponding a uniform northeastward f ow. In additionto this, we consider three abrupt events in which the relative f ow changes speedand direction. For a total simulation time of 6 days, the firs event occurs at time zeroand produces a change of the relative f ow of (Δu f , Δv f ) = (10 cm/s, 0 cm/s). Thesecond event takes place at day 2 and produces a f ow change of (Δu f , Δv f )=Fig. 3.25 Pathway of a flui parcel carried by an ambient f ow and subject to inertial oscillations