56
3 Basics of Geophysical Fluid Dynamics
3.14.7 Inertial Oscillations
The aim of this section is to predict the pathway of a non-buoyant parcel floatin
with an ambient uniform fl w (U o , V o ) subject to a series of abrupt wind events. The
momentum equations governing this problem can be formally written as:
∂u
∂t
= + f v +
∂u f
∂t
(3.55)
∂v
∂t
= − f u +
∂v f
∂t
(3.56)
where u f and v f are forcing terms assumed to be uniform in space. The pathway of
the flui parcel can then be calculated from:
dx
dt
= U o + u and
dy
dt
= V o + v
(3.57)
To illustrate this process, we consider an ambient fl w with velocity components
of (U o , V o ) = (5 cm/s, 5 cm/s), corresponding a uniform northeastward f ow. In addition to this, we consider three abrupt events in which the relative f ow changes speed
and direction. For a total simulation time of 6 days, the firs event occurs at time zero
and produces a change of the relative f ow of (Δu f , Δv f ) = (10 cm/s, 0 cm/s). The
second 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