Rocky Mountain Simulation

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 of ~1.5% is used to coarsen the mesh as the lateral boundaries are approached. The domain extends to an altitude of 140 km and uses uniform vertical spacing of 250 m. A total of 768 x 460 x 560 mesh points are used. Inviscid wall boundary conditions are used and the surface whereas characteristic (radiative) conditions are used at the lateral and top boundaries.

Wind and Thermodynamic Profiles

The mean wind and temperature profiles are taken from radiosonde data on February 19th, 2016, from launch site in Grand Junction. These profiles extend to an altitude of 31 km. MERRA2 wind profiles are used above the radiosonde measurements to an altitude of 80 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. The temperature is extended using the NRLMSIS Atmosphere Model (Composition). Plots of various profiles are shown below.

Wind Condition

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 radiosonde-measured values over a period of two hours. The forcing terms follow a hyperbolic tangent function in time, which results in very gentle acellerations 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

Animation of w' in the xz plane at the position y = -20 km

The following two animations provide an overview of the wave motion as imaged in a meridional-altitude (xz) plane. The solution is rater uninteresting during the initial phase of the wind ramping and thus the animations begin at the one hour mark. At this time weak disturbances are seen near the surface but these quickly grow to yield an orographic wave pattern. Turbulence develops near the surface at a time of about 1.5 hours and wave breaking at about 16 km commences at a time of about 1.8 hours. Fast-running secondary acoustic waves are seen near the upper boundary shortly thereafter. A complex secondary wave pattern then develops and strengthens over the next four hours. A second breaking zone develops at 110 km at a time of about 5 hours and persists till the end of the simulation. A mixture of secondary and tertiary waves are seen between 110 km and the domain top at 140 km.

Primary wave breaking can be seen in the following animations on a horizontal cross-section at an altitude of 21 km. Secondary waves from the turbulence below are first seen at 1.9 hours. Shortly thereafter turbulence develops in the image plane and becomes quite widespread as the simulation progresses.

Secondary wave activity can be seen in the following animations on a horizontal cross-section at an altitude of 110 km. There is very little activity up to a time of 2 hours when the acoustic blast due to the onset of wave breaking appears. A mixture of acoustic and gravity waves then appears and strengthens over the next three hours. Then at about 5 hours turbulenc first appears as the secondary gravity waves themselves break. The region of turbulence then steadly increases up to the end of the simulation.

Since the fields were still changing in time at 6 hour mark shown in the animations above, the simulation was continued out to a time of 10 hours. The main insights available from the later time period is that the secondary wave breaking zone at 110 km extends to nearly fill the entire horizontal domain. The tertiary waves also strengthen and become visibly distinct from the residual secondary waves that also occupy the region between 110 and 140 km.