Rocky Mountain Simulations
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 7o 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.
The mesh is clustered in both horizontal directions in order to achieve
1000 x 1000 meter spacing over the mountain range in the region shown by
the black rectangle. Very weak stretching is used so that the resolution
is still ~1000 x 1000 m over the high planes east of the range. The domain
extends to an altitude of 48 km and uses uniform vertical spacing of 1000 m.
A total of 280 x 260 x 48 mesh points are used. Sponge layers are used
on all external boundaries in order to absorb outgoing waves.
Wind and Thermodynamic Profiles
Wind and Thermodynamic Profiles
The mean winds and temperature profile are taken from radiosonde data, on
three dates in February 2020, from a launch site in Grand Junction,
Colorado. These profiles extend to an altitude slightly more than 30 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 three separate balloon
measurements are shown below. Note that each profile is resampled on
the 1000m mesh spacing.
Feb 01 Feb 10 Feb 20
Wind Condition
Feb 01 Feb 10 Feb 20
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 three simulation hours. u' and w' are shown for each wind profile.