This page describes a numerical simulation of gravity waves over the Rocky
Mountains in Colorado.

Computational Domain

The layout of the of the simulation is shown in the figure below. Note that the computational
domain (thin white line) is rotated at 7^{o} with respect to lines of constant
latitude.

Just the computational domain is shown in the figure below. In this plot,
and those that follow the results are shown in the computational frame.
The terrain is damped around the domain edges in order to
achieve a fixed elevation around the perimeter.

A linear balloon flight path is depicted based on an average wind direction of
250 degrees launched from Grand Junction, Colorado.

The mesh is clustered in both horizontal directions in order to achieve
250 x 250 meter spacing over the mountain range in the region shown by
the black rectangle. Weak stretching is used so that the resolution
is still ~250 x 250 m over the eastern mountains. The domain
extends to an altitude of 48 km and uses uniform vertical spacing of 250 m.
A total of 800 x 500 x 192 mesh points are used. Sponge layers are used
on all external boundaries in order to absorb outgoing waves.

Wind and Thermodynamic Profiles

The mean winds and temperature profile are taken from radiosonde data on
February 20th, 2020, from launch site in Grand Junction.
These profiles extend to an altitude of 23.4 km. A
third order interpolating polynomial is then used to smoothly extend the
winds above this altitude using the condition that U=V=0 at the upper
boundary. Plots of various profiles for the balloon
measurements are shown below. Note that each profile is resampled on
the 250m mesh spacing.

Wind Condition

The mean winds near the surface are increased in time.
Forcing terms gradually introduce winds near the surface with the
objective of achieving the wind profile within a two hour period.
A hyperbolic tangent function is used in order to produce gentle
acceleration of the wind 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.

Results

Each animation is run for four simulation hours. u' and w' and vorticity magnitude
are shown.

Animation of u' in the xz plane at the position y = 0

Animation of w' in the xz plane at the position y = 0 km

Animation of vorticity magnitude in the xz plane at the position y = 0 km

Animation of u' in the xz plane at the position y = 50

Animation of w' in the xz plane for the last hour at the position y = 50 km

Animation of vorticity magnitude in the xz plane at the position y = 50 km

Animation of u' in the xy plane at the altitude z = 30

Animation of w' in the xy plane at the altitude z = 30 km

Animation of vorticity magnitude in the xy plane at the altitude z = 30 km overlayed on the computational domain