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6.6  PASS: Coriolis formulation in 3-D

Sébastien Delaux
sh coriolis.gfs
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coriolis.gfs (view) (download)
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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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