Previous: Theoretical formulation Next: Conclusions Up: Ext. Abst.

 

Numerical simulations

In the middle atmosphere, the wind perturbations are composed of wave packets coming from several tropospheric sources, such as mountains, convective and frontal activity, breaking of mountain waves, shear instabilities, geostrophic adjustment of the jet stream, which have different characteristic propagation speeds.

To model this situation, we assume that a superposition of wave packets is found in the region of interest, each packet of the form (6) having a range of horizontal wave speeds between $c_2=N m_{02}^{-1}$ and $c_1=N m_{01}^{-1}$.

In this representation a broad spectrum in the initial vertical wavenumber has also a broad spectrum in frequency through the dispersion relation, while in the horizontal wavenumber the spectrum is monochromatic. Note that $k$ remains unaltered during the whole wave propagation. An extension of this formulation to include packets in $k$ can also be made as long as the wave spectra are separable. At the present stage of development we have chosen to present only the monochromatic scenario where the main physical process are clearer specially for conceptual purposes.

Figure: Plots on the left: Horizontal wind perturbation belonging to a superposition of wave packets given by (7). Background conditions: $N=0.01  s^{-1}$ $d_z U=(30:upper,  10:middle,  2:lower)  m/s  (10 km)^{-1}$. Plots on the right: Mean power spectrum for 100 profiles simulated with the model. The dashed line represents the mean of the power spectra by Fourier; full line shows the mean of the theoretically predicted spectral tail with a $-3$ power law.
\includegraphics[width=3in]{fig/fig11.eps}
\includegraphics[width=3in]{fig/fig12.eps}
\includegraphics[width=3in]{fig/fig13.eps}
\includegraphics[width=3in]{fig/fig14.eps}
\includegraphics[width=3in]{fig/fig15.eps}
\includegraphics[width=3in]{fig/fig16.eps}

Each generated profile contains 15 wave packets, 10 terminating inside of the interest region and 5 terminating above this region. The exact place of termination is random within an interval. In this way we determine the parameter $m_{02}$.

From the rest of the free parameters of the wave packets, the amplitude $u_0$, and the initial phase are taken randomly within a reasonable interval, in a way similar to Chimonas, 1997 while the width of the spectrum which has also been taken at random within an interval ( $\lambda_z=400 m$ to $\lambda_z=1000 m$) in order to produce a reasonable perturbations. Note that it is impossible to isolate a wave packet in an observed wind perbutation profile in order to determine the spectral width. In future work it would be possible to estimate this parameter in a somewhat indirect way from profiles, if their effects on the observed vertical power spectrum through Doppler shifting are taken into account.

Figures 5, 7 and 9 show characteristic wind profiles for background conditions given by $N=0.01 s^{-1}$ and $d_z U=( 30,  10,  2) m s^{-1} (10 km)^{-1}$, ( $Ri= 11.1, 100, 2500$), respectively. There is a high correspondence between the numerically generated profiles and actual profiles.

For the weakest shear case the PS goes to the -3 predicted tail for higher wavenumbers because it has higher initial wavenumbers and the asymptotic behavior is satisfied for $m>m_{0}$ (See (16)). The spectral knee has also a mean shear dependence, the higher the shear the greater the characteristic wavenumber. The quantitative values may be strongly altered in a more realistic picture (interactions between components, time dependences, etc.).

Previous: Theoretical formulation Next: Conclusions Up: Ext. Abst.