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6.6  PASS: Coriolis formulation in 3-D

Author
Sébastien Delaux
Command
sh coriolis.sh coriolis.gfs
Version
100621
Required files
coriolis.gfs (view) (download)
coriolis.sh
Running time
30 seconds

This test case is taken from the test cases of the Advanced Regional Prediction System [7]. A Coriolis term is applied to a cubic domain with periodic boundary conditions in the x, y and z directions. Provided the flow has a unidirectional initial velocity field and a zero initial pressure perturbation, the spatial derivatives are initially zero and a solution exists to the Navier-Stokes equations for which spatial derivatives are zero at all times.

In this case the velocity field is given by:

u = A cos(2Ω t) + B sin(2Ω t)
v = − A sinΦ sin(2Ω t) + B sinΦ cos(2Ω t) + C
w = A cosΦ sin(2Ω t) − B cosΦ cos(2Ω t) + D

where A, B, C and D are constants of integration:

A = U0
B = sinΦ V0 − cosΦ W0
C = cosΦ 
cosΦ V0 + sinΦ W0 
D = sinΦ 
cosΦ V0 + sinΦ W0 

Here Φ = π/2 so that the z component of the Coriolis force is equal to zero. Figure 69 shows the evolution of the three components of the velocity with time.


Figure 69: Evolution of the velocity with time. The solid lines are the analytical solution.


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