5.9 The Equatorial Barrier
155
first sub-time step can be calculated from:
Δt min =
1
u
x
ln
δx edge u
x
u w + δx
∗
i u
x
+ 1
In distance to the respective boundary δx edge is defined as δx edge = Δx − δx
∗
i for
eastward flow and as δx edge = −δx
∗
i for westward flow.
For the case of Lagrangian floats, turbulence is described by the probability that
a particle is shifted a certain distance within a given time step (Maier-Reimer and
S¨ undermann, 1982). After Maier-Reimer (1980), maximum diffusive velocities can
be related to eddy diffusion coefficients. In the x-direction, for instance, this relationship reads:
u max =
6A h
Δt
Turbulent velocity fluctuations can then be determined for each float with the
Monte-Carlo method which consists of multiplying each maximum current component by a random generated number between −1 and 1. A displacement equation of
the form of Eq. (5.19) can be adopted to include turbulence effects on float motions.
Computer codes of this book only use the simple averaging method for float
predictions and ignore effects of turbulence. The implementation of more advanced
float tracking schemes remains for the reader.
5.9 The Equatorial Barrier
5.9.1 Inertial Oscillations About the Equator
A flow crossing the equator experiences a change of sign of the Coriolis force and
therefore becomes deflected back towards the equator (Fig. 5.25). It then again overshoots the equator owing to its inertia, and the Coriolis force on the other side of the
equator moves it back, and so on, in an oscillatory fashion. This unique behavior,
in which the equator acts as a waveguide, is the signature of inertial oscillations
about the equator. Whereas inertia oscillations in off-equatorial regions are associated with closed flow trajectories (in the absence of ambient flow), those centred on
the equator are always associated with a net eastward flow. The period of equatorial
inertial oscillations is approximately given by (e.g., Cushman-Roisin, 1994):
T eq =
1
√ β V o
(5.21)
where β is the meridional variation of the Coriolis parameter at the equator (β ≈
2.28 × 10
−11 m
−1 s
1 ), and V o is the initial speed of the flow crossing the equator.
With V o = 0.2 m/s, Eq. (5.21) yields 5.4 days. The radius of the half-circle paths of
155
first sub-time step can be calculated from:
Δt min =
1
u
x
ln
δx edge u
x
u w + δx
∗
i u
x
+ 1
In distance to the respective boundary δx edge is defined as δx edge = Δx − δx
∗
i for
eastward flow and as δx edge = −δx
∗
i for westward flow.
For the case of Lagrangian floats, turbulence is described by the probability that
a particle is shifted a certain distance within a given time step (Maier-Reimer and
S¨ undermann, 1982). After Maier-Reimer (1980), maximum diffusive velocities can
be related to eddy diffusion coefficients. In the x-direction, for instance, this relationship reads:
u max =
6A h
Δt
Turbulent velocity fluctuations can then be determined for each float with the
Monte-Carlo method which consists of multiplying each maximum current component by a random generated number between −1 and 1. A displacement equation of
the form of Eq. (5.19) can be adopted to include turbulence effects on float motions.
Computer codes of this book only use the simple averaging method for float
predictions and ignore effects of turbulence. The implementation of more advanced
float tracking schemes remains for the reader.
5.9 The Equatorial Barrier
5.9.1 Inertial Oscillations About the Equator
A flow crossing the equator experiences a change of sign of the Coriolis force and
therefore becomes deflected back towards the equator (Fig. 5.25). It then again overshoots the equator owing to its inertia, and the Coriolis force on the other side of the
equator moves it back, and so on, in an oscillatory fashion. This unique behavior,
in which the equator acts as a waveguide, is the signature of inertial oscillations
about the equator. Whereas inertia oscillations in off-equatorial regions are associated with closed flow trajectories (in the absence of ambient flow), those centred on
the equator are always associated with a net eastward flow. The period of equatorial
inertial oscillations is approximately given by (e.g., Cushman-Roisin, 1994):
T eq =
1
√ β V o
(5.21)
where β is the meridional variation of the Coriolis parameter at the equator (β ≈
2.28 × 10
−11 m
−1 s
1 ), and V o is the initial speed of the flow crossing the equator.
With V o = 0.2 m/s, Eq. (5.21) yields 5.4 days. The radius of the half-circle paths of