Anelastic/Compressible GW Comparison
Simulation results from the Lipps and Hemler Anelastic formulation and the
full compressible equations are compared for a GW packet, localized in the
vertical direction. The simulation domain extends from 75 to 275 km in
altitude and from 0 to 20 km in the horizontal direction. The mesh is uniform
with equal spacing of 200 m in both the horizontal and vertical directions.
The background thermodynamic state is isothermal with a temperature of 600 k,
which gives a scale height of 17.6 km and a buoyancy period of ~500 sec.The GW has lambda_x = lambda_z = 20 km, so that the intrinsic frequency is N/sqrt(2), or tau_w = sqrt(2)*tau_b ~700 sec. The horizontal and vertical phase speeds are equal at 28.4 m/s. Initial conditions for the packets are formed by multiplying the respective anelastic and compressible linearized GW solutions by a Gaussian function of half-width 20 km, centered at 80 km in altitude. The vertical group velocity for the packet is ~0.5*c_z = 14.1 m/s. The maximum initial non-dimensional amplitude of the packet is 0.2.
The simulations are run for 5800 seconds of physical time, which corresponds to ~8.25 wave periods. Images for the movies shown below are taken at 58 second intervals, or 0.0825 wave periods.
The anelastic simulation makes use of a slip wall boundary conditions at the lower boundary and a radiation condition at the upper boundary. The compressible formulation uses slip wall conditions at both boundaries in conjunction with sponge layers of thickness 20 km. It was found that a sponge at the lower boundary was required in order to absorb the suprisingly large acoustic starting transient.
The movies below show a side-by-side comparison of the anelastic and compressible results. In all cases the anelastic results are on the left and the compressible results are on the right.
Animation of GW fields. From left to right, vertical velocity, potential
temperature, and vorticity magnitude. Click on an image to start the
movie. Links to zip files containing the images from the movies are provided
below each movie image.
| Vertical Velocity | Potential Temperature | Vorticity Magnitude |
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| w images | theta images | vorticity magnitude images |
| w movie avi format |
theta movie avi format |
vorticity magnitude movie avi format |