New Zealand Simulation
This page describes a numerical simulation of gravity waves over New Zealand's
south island. Primary orographic waves break at an altitude of about 80 km,
thereby generating secondary waves. The secondary waves are filtered by
viscous effects, but the longer wavelengths propagate to altitudes in excess
of 400 km.
Computational Domain
The layout of the of the simulation is shown in the figure below. The origin is located at
Mount Cook (43.5950° S, 170.1418° E).
The computation grid uses horizontal mesh spacings of 500 m in a region slightly
larger than the south island land mass. The mesh is then stretched gently to
the lateral boundaries. The vertical grid uses uniform spacing of 500 m up to
an altitude of 140 km. Beyond 140 km the mesh is subdivided into four
additional zones where the vertical grid is continuously stretched, but the
horizontal spacings jump by a factor of two across each interface. The
interfaces are located at 140, 200, 260 km, and the horizontal mesh
spacing increases from 500 m in the lowest zone to 1, 2, and 4 km in the
progressively higher zones. The vertical mesh spacing increases continuously
from an altitude of 140 km to the domain top at 320 km. The vertical spacing
at the domain top is 3.3 km. Inviscid wall boundary conditions are used and
the surface whereas characteristic (radiative) conditions are used at the
lateral and top boundaries.
Wind Profiles
The background winds and temperature are fixed in space and time.
The plots below show representative profiles for point located at 45.5°S, 170°E.
This maps to (-11.2,-210.8) km in grid space, slightly SSE of Lauder (-36.8,-160.9).
Forcing
In order to minimize starting transients, the mean winds are damped to zero
between the surface and 30 km. Forcing terms are then used to increase the
near-surface winds to the NAVGEM-provided values over a period of four
hours. The forcing terms follow a hyperbolic tangent function in time, which
results in very gentle accelerations near the beginning and end of the forcing
period. The maximum forcing rate is equivalent to that of a linear ramp
with a duration of one hour.
The following animations provide an overview of the wave motion as imaged in meridional-altitude (xz) planes.
Wind Profiles
The background winds and temperature are fixed in space and time.
The plots below show representative profiles for point located at 45.5°S, 170°E.
This maps to (-11.2,-210.8) km in grid space, slightly SSE of Lauder (-36.8,-160.9).
Forcing
In order to minimize starting transients, the mean winds are damped to zero
between the surface and 30 km. Forcing terms are then used to increase the
near-surface winds to the NAVGEM-provided values over a period of four
hours. The forcing terms follow a hyperbolic tangent function in time, which
results in very gentle accelerations near the beginning and end of the forcing
period. The maximum forcing rate is equivalent to that of a linear ramp
with a duration of one hour.Animation in xz planes
The following animations provide an overview of the wave motion as imaged in meridional-altitude (xz) planes.
y = -250 km
Results in xy planes
Primary wave breaking can be seen in the following animations on a horizontal
cross-section at an altitude of 90 km. Wave breaking begins at a time of
about 11:00 UTC and then becomes more widespread as time advances. Since the
wave breaking zone extends to lower altitude, secondary waves from the
turbulence at lower altitudes are also visible.