This page describes a numerical Simulation of waves over the Owen's Valley
generated by winds over the Sierra Nevada Mountain Range.
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
300 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,
which is rotated 300 with respect to earth longitude/latitude
coordinates. 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 Sierra Nevada mountain range. Very
weak stretching is used so that the resolution is still ~1000x1000 m over
the Owen's valley. The domain extends to an altitude of 96 km and uses
a uniform vertical spacing of 1000 m. A total of 200 x 440 x 96 mesh points
are used. Sponge layers are used on all external boundaries in order
to absorb outgoing waves.
Wind and Thermodynamic Profiles
Wind and temperature profiles were taken from the climatology study of
Fleming et al. (1988) for February at 400 N. This is the same
data that was used by Woods and Smith (2011). The climatology does not
provide profiles of meridional wind so that component was simply set to
zero. Plots of the various profiles are shown below.
Mean wind evolution
Here the winds are initially set to zero from the surface to an altitude of
about 20 km. At this point the wind transitions to the profiles shown in the
plots above.
Forcing terms then gradually introduce winds near the surface with the
objective of achieving the profile shown above 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 45 minutes.
Animation of u' in the xz plane at the position of maximum mountain height
Animation of u' in the xy plane at an altitude of 85 km
Animation of w' in the xy plane at an altitude of 85 km