3.14 Exercise 4: The Coriolis Force in Action
55
3.14.4 Improved Scheme 2: The Local-Rotation Approach
The Coriolis force operates at a right angle to velocity and does not change the
speed of motion, only the direction. Hence, this feature can be simulated by a local
rotation of the velocity vector; that is,
u
n+1
= cos(α)u
n
+ sin(α)v
n
,
(3.53)
v
n+1
= cos(α)v
n
− sin(α)u
n
(3.54)
From geometric considerations, the rotation angle can be determined at α = 2
arcsin (0.5Δt f ). For Δt | f | << 1, this can be approximated by α ≈ Δt f .
3.14.5 Yes!
Figure 3.24 shows the results using the semi-implicit scheme demonstrating that we
are now able to successfully simulate inertial oscillations in a rotating fluid With
this code, the reader is encouraged to explore inertial oscillations for a variety of
situations, such as for different geographical locations and different initial locations
and speeds. The code also includes a formulation of the local-rotation approach with
α ≈ Δt f that can be selected via the parameter “mode”.
3.14.6 Sample Code and Animation Script
The FORTRAN code for this exercise, called “Coriolis f95”, and the SciLab script,
“Coriolis.sce” can be found in the folder “Exercise 4” on the CD-ROM. The fil
“info.txt” contains additional information.
Fig. 3.24 Snapshots of the trajectory (white line) of a water parcel subject to the Coriolis force as
predicted with the semi-implicit approach. The star denotes a reference location in the fi ed frame
of reference
55
3.14.4 Improved Scheme 2: The Local-Rotation Approach
The Coriolis force operates at a right angle to velocity and does not change the
speed of motion, only the direction. Hence, this feature can be simulated by a local
rotation of the velocity vector; that is,
u
n+1
= cos(α)u
n
+ sin(α)v
n
,
(3.53)
v
n+1
= cos(α)v
n
− sin(α)u
n
(3.54)
From geometric considerations, the rotation angle can be determined at α = 2
arcsin (0.5Δt f ). For Δt | f | << 1, this can be approximated by α ≈ Δt f .
3.14.5 Yes!
Figure 3.24 shows the results using the semi-implicit scheme demonstrating that we
are now able to successfully simulate inertial oscillations in a rotating fluid With
this code, the reader is encouraged to explore inertial oscillations for a variety of
situations, such as for different geographical locations and different initial locations
and speeds. The code also includes a formulation of the local-rotation approach with
α ≈ Δt f that can be selected via the parameter “mode”.
3.14.6 Sample Code and Animation Script
The FORTRAN code for this exercise, called “Coriolis f95”, and the SciLab script,
“Coriolis.sce” can be found in the folder “Exercise 4” on the CD-ROM. The fil
“info.txt” contains additional information.
Fig. 3.24 Snapshots of the trajectory (white line) of a water parcel subject to the Coriolis force as
predicted with the semi-implicit approach. The star denotes a reference location in the fi ed frame
of reference