This page describes a numerical simulation of waves generated by winds
blowing over a section of the Antarctic Peninsula. The mean winds and
temperature profile were supplied by Steve Eckermann. These
profiles only extent to an altitude of 103 km so the winds were adjusted by
adding a Gaussian-shaped lobe with maximum velocity equal to 120% of the
maximum contained in the profile below 103 km. The center and width of the
Gaussian are determined so that the value and slope of the winds are
matched with with the data at z=103 km. The temperature profile was
smoothly extended to a maximum temperature of 800 degrees K via a hyperbolic
tangent profile. Again, the width and center for the hyperbolic tangent
are determined so that the temperature and its derivative match the data at
and altitude of z=103 km. The wind, temperature, and N^2 profiles are
shown below.
The simulation makes use of a terrain map for the Southern Andes covering
a latitude range of 55.6 S to 74.6 S and a longitude of 40.6 W to 85.8 W.
This map is shown below.
A window function is then used to flatten the terrain on the Antarctic
mainland. The coordinates are also rotated clockwise by 40 degrees so
that the peninsula is roughly aligned with the y' axis. These operations
result in the following modified terrain map.
The domain extends 1500 km in the x' direction and 1500 km
in the y' direction. The grid is clustered in the region of terrain,
having 500 m resolution in the x' direction and 1000 m in the y' direction.
The vertical mesh is uniform with spacing 500 m from the surface to an
altitude of 120 km. Above 120 km, the vertical mesh is gradually stretched
such that the spacing at the upper boundary is 1750 m. A total of
820 X 1050 X 320 mesh points are used in the x', y', and z directions
respectively.
The lower boundary is treated as a slip wall whereas radiation conditions in concert with a sponge is used at all other boundaries. The sponge/radiation condition produces solutions where little or no wave energy reflects (or enters) at the boundaries.
The simulation is started from rest and the wind is increased according to a hyperbolic tangent function over a period of 40 minutes.
Click on the images below to see animations of the u and w velocity perturbations as well as the vorticity magnitude, visualized in the x'-z plane at the middle of the domain. The color map in each of these animations is changed several times during the animation in order to accommodate the large increase in wave amplitude with time. These rescalings result in somewhat annoying jumps, but at least it is possible to visualize the entire evolution.
The lower boundary is treated as a slip wall whereas radiation conditions in concert with a sponge is used at all other boundaries. The sponge/radiation condition produces solutions where little or no wave energy reflects (or enters) at the boundaries.
The simulation is started from rest and the wind is increased according to a hyperbolic tangent function over a period of 40 minutes.
Click on the images below to see animations of the u and w velocity perturbations as well as the vorticity magnitude, visualized in the x'-z plane at the middle of the domain. The color map in each of these animations is changed several times during the animation in order to accommodate the large increase in wave amplitude with time. These rescalings result in somewhat annoying jumps, but at least it is possible to visualize the entire evolution.
Animations in the x-z plane
Animations in the x-y plane at z=40 km
Animations in the x-y plane at z=175 km