All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig1.eps} \end{figure}$ Figure 1: The evolution of SFH normalized velocity and density perturbations ( $v_x/c_{\rm s}$ , $~v_y/c_{\rm s}$ and $~D \equiv{\rm i} \varrho/\rho_0$ ) and its normalized energy $(E_{\vec k}(t)/E_{\vec k}(0))$ at $R_{\rm max}=1.06$ (m=R/H in terms of the azimuthal wavenumber). In the dynamics of the initially imposed vortex SFH (with k_x(0)/k_y = -15, k_y=1) transient growth is dominant, but the wave generation starts to be noticeable.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig2.eps} \end{figure}$ Figure 2: The evolution of SFH normalized velocity and density perturbations ( $v_x/c_{\rm s}$ , $v_y/c_{\rm s}$ , D) and its normalized energy $(E_{\vec k}(t)/E_{\vec k}(0))$ at $R_{\rm max}=1.34$ ( m = 0.5 R/H in terms of the azimuthal wavenumber). Evolving in the shear flow, the initially imposed vortex mode SFH (with k_x(0)/k_y = -15, k_y=0.5), gaining energy from the mean flow and amplifying, retains its aperiodic nature until k_x(t )/k_y<0. After time t^*=10 (at which k_y(10)=0), we observe the appearance of the wave SFH.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig3.eps} \end{figure}$ Figure 3: The dynamics of $v_x/c_{\rm s},~ v_y/c_{\rm s},~D$ , their vortex $(v_x^{\rm (v)}/c_{\rm s},~ v_y^{\rm (v)}/c_{\rm s},~ D^{\rm (v)})$ and wave parts $(v_x^{\rm (w)}/c_{\rm s},~ v_y^{\rm (w)}/c_{\rm s},~ D^{\rm (w)})$ for a pure vortex initial perturbation ( $v_x^{\rm (w)}(0),~ v_y^{\rm (w)}(0),~ D^{\rm (w)}(0) = 0$ ) with the same parameters as in Fig. 2. The process may be interpreted as an abrupt emergence of wave SFH from the related vortex SFH at t = t^*. The amplitude of the generated wave $v_y^{\rm (w)}(t^*)$ smoothes the jump in the aperiodic mode (see Eq. (39)).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig4.eps} \end{figure}$ Figure 4: Simple sketch of the relation between the Rossby wave and vortex mode perturbations in the wavenumber plane (K_x, K_y), see details in the text.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1046fig5a.eps}\hspace*{4mm} \includegraphics[width=7.5cm,clip]{1046fig5b.eps} \end{figure}$ Figure 5: Images of the initial density ( left plot) and vorticity ( right plot) distributions with enlargements of the vortex area.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig6.ps} \end{figure}$ Figure 6: Evolution of the vorticity distribution for case A. The six panels show the vorticity distributions at six different times. The times are respectively t = 0.31, 1, 2, 3.12, 4.5, 6.31. At late times the vorticity distribution in the inner region becomes quite noisy, however one has to take into account that the calculation of vorticity implies a numerical differentiation operation that amplifies the error, larger here due to the grid deformation
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig7.ps} \end{figure}$ Figure 7: Evolution of the density distribution for case A. The six panels show the density distributions at six different times, t = 0.31, 1, 2, 3.12, 4.5, 6.31.
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{1046fig8.ps} \end{figure}$ Figure 8: Ray trajectories superimposed on the density distribution for case A at time t = 2. The different rays correspond to different values of $k_{\theta }$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{1046fig9.ps} \end{figure}$ Figure 9: Ray trajectories superimposed on the density distribution for case C at time t = 2. The different rays correspond to different values of $k_{\theta }$ . In the image we show also a vortex in a symmetric position for better comparison. Note that in case C the computational domain covers the radial interval 0.5 < r < 1.5.
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{1046f10.ps} \end{figure}$ Figure 10: Ray trajectories superimposed on the density distribution for case A at time t = 3.75. The different rays correspond to different values of $k_{\theta }$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046f11.ps} \end{figure}$ Figure 11: Comparison of the four different cases at the same time. The four panels show images of the density distribution for cases A ( top left), B ( top right), C ( bottom right) and D ( bottom left) at t = 2.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1046f12.ps} \end{figure}$ Figure 12: Longer time evolution for case A. The three panels show images of the density distributions at three different times; from top to bottom the times are respectively t = 8.12, 11.25, 14.5.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{1046f13.ps} \end{figure}$ Figure 13: Energy normalized to the initial value versus time for the cases A, B and D (the solid line refers to case A, the dotted curve to case B and the dashed curve to case D).
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1046f14.eps} \end{figure}$ Figure 14: Plot of the total mass that has flown through radius r at time t versus time, for case A. This figure refers to radial positions that are immediately inside (r = 0.875, solid line) and immediately outside (r = 1.125, dashed line) the vortex.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1046f15.eps} \end{figure}$ Figure 15: Total mass that has flown through radius r at time t versus time, for case A. This figure refers to r = 0.1.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig4.eps} \end{figure}$	Figure 4: Simple sketch of the relation between the Rossby wave and vortex mode perturbations in the wavenumber plane (K_x, K_y), see details in the text.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1046fig5a.eps}\hspace*{4mm} \includegraphics[width=7.5cm,clip]{1046fig5b.eps} \end{figure}$	Figure 5: Images of the initial density ( left plot) and vorticity ( right plot) distributions with enlargements of the vortex area.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046fig7.ps} \end{figure}$	Figure 7: Evolution of the density distribution for case A. The six panels show the density distributions at six different times, t = 0.31, 1, 2, 3.12, 4.5, 6.31.
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$\begin{figure} \par\includegraphics[width=6.5cm,clip]{1046fig8.ps} \end{figure}$	Figure 8: Ray trajectories superimposed on the density distribution for case A at time t = 2. The different rays correspond to different values of $k_{\theta }$ .
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$\begin{figure} \par\includegraphics[width=6.5cm,clip]{1046fig9.ps} \end{figure}$	Figure 9: Ray trajectories superimposed on the density distribution for case C at time t = 2. The different rays correspond to different values of $k_{\theta }$ . In the image we show also a vortex in a symmetric position for better comparison. Note that in case C the computational domain covers the radial interval 0.5 < r < 1.5.
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$\begin{figure} \par\includegraphics[width=6.5cm,clip]{1046f10.ps} \end{figure}$	Figure 10: Ray trajectories superimposed on the density distribution for case A at time t = 3.75. The different rays correspond to different values of $k_{\theta }$ .
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1046f11.ps} \end{figure}$	Figure 11: Comparison of the four different cases at the same time. The four panels show images of the density distribution for cases A ( top left), B ( top right), C ( bottom right) and D ( bottom left) at t = 2.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1046f12.ps} \end{figure}$	Figure 12: Longer time evolution for case A. The three panels show images of the density distributions at three different times; from top to bottom the times are respectively t = 8.12, 11.25, 14.5.
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{1046f13.ps} \end{figure}$	Figure 13: Energy normalized to the initial value versus time for the cases A, B and D (the solid line refers to case A, the dotted curve to case B and the dashed curve to case D).
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1046f14.eps} \end{figure}$	Figure 14: Plot of the total mass that has flown through radius r at time t versus time, for case A. This figure refers to radial positions that are immediately inside (r = 0.875, solid line) and immediately outside (r = 1.125, dashed line) the vortex.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1046f15.eps} \end{figure}$	Figure 15: Total mass that has flown through radius r at time t versus time, for case A. This figure refers to r = 0.1.
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