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.

Vertical Velocity |
Potential Temperature |
Vorticity Magnitude |

w images | theta images | vorticity magnitude images |

w movie avi format |
theta movie avi format |
vorticity magnitude movie avi format |