New Zealand Simulation

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, 320 km, and the horizontal mesh spacing increases from 500 m in the lowest zone to 1, 2, 4, and 8 km in the progressively higher zones. The vertical mesh spacing increases continuously from an altitude of 140 km to the domain top at 440 km. The vertical spacing at the domain top is 5.6 km. Inviscid wall boundary conditions are used and the surface whereas characteristic (radiative) conditions are used at the lateral and top boundaries.

Coarse Grid Comparison

A coarser grid with x-y spacing of 4km and 1km vertical in the unitform regions is used for comparison. Only a single interface is used such that the grid spacing at the top of the domain is the same as the full simulation.

Wind Profiles

The background winds and temperature vary in both space and time as predicted by a NAVGEM reanalysis run. The NAVGEM data is sampled on a 1° by 1° grid and hourly in 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 22 km. Forcing terms are then used to increase the near-surface winds to the NAVGEM-provided values over a period of two 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 thirty minutes.

Simulation Results Followed by Coarse Domain

Animation in xz planes

The following animations provide an overview of the wave motion as imaged in meridional-altitude (xz) planes. The solution is rater uninteresting during the wind ramping phase and thus the animations begin two hours into the simulation, which corresponds to 10:00 UTC for the measurements. The primary orographic waves break shortly after the start of the animation and immediately launch a system of strong acoustic waves. As time goes on a mixture of acoustic and gravity waves appear and these propagate all the way to the domain top at an altitude of 440 km.

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.

Secondary waves can be seen in the following animations on a horizontal cross-section at an altitude of 250 km. The large blast shortly after 10:00 UTC is due to numerical problem that produced a discontinuity in the solution when the forcing ended. Unfortunately this glitch pollutes the upper-altitude solution for some time, but clear secondary wave patterns are visible by about 11:000 UTC. The waves strengthen over time and are composed of a mixture of both acoustic and gravity wave modes.

The results look similar on a horizontal plane at an altitude of 320 km. The main difference is that the waves are somewhat weaker and are larger in scale.