1.
Design of the Numerical Experiment
Numerical simulations for
uniform flows over a circular cylinder were conducted to
examine the laterial boundary conditions implemented in
FVCOM.
This problem was tested
under a nonrotating and homogenuous density conditions for
a rectangular channel with a width of 15m, a length of 60m
and a constant depth of 0.5m (Fig. 1). The center of a circular
cylinder(D=1m) is located at half witdth of the channel
with a distance of 16.5m to the left side which minimizes
effects from laterial boundary and outflow conditions. Due
to low flowing speed and shallow water, only a horizontal
two dimensional FVCOM was set up for the simulations. The
model was forced by a unifom, constant flow from west boundary
(upstream).
Fig.1: View of the computing domain and zoom view of the
grid aroud the cylinder

2. Results
A Reynolds number (Re =
UD/ν, where U is the upstream velocity and ν is the
molecular kinematic viscosity) can be defined for the above
test to characterize the flowing features behind the obstacle.
As described in classical fluid dynamics text, if Re<40,
a laminar flow with two steady symmetric vortices behind
the cylinder is obtained; while for 40<Re<1000, a
periodic vortex pairs shed from the downstream side of the
cylinder. In case1, case2 and case3, the inflow velocity
was adjusted to obtain a desired Reynolds number.
Case1:
Laminar
flow with two steady vortices behind the cylinder
(Re < 40)

color plot represent relative vorticity
(click the figure for animation)

Case2:
Shear instability
occurs at Re around 40

color plot represent relative vorticity
(click the figure for animation)

Case3:
Kármán
vortex street (Re around 300)

color plot represent relative vorticity
(click the figure for animation)

Case4:
The
above test was further extended to a geostrophic
scale island wakes problem following the work of
Dong et al,(2006). Only Coriolis force was considred
at current stage simulation, so again a uniform
inflow of 0.2m/s was enforced from boundary. With
the inclusion of a constant Coriolis frequency (f=10^4
s^1), the results showed the vortex shedding becomes
unsymmetric with a deflection to the right direction.

color plot represent relative vorticity
(click the figure for animation)

