All Figures

$\begin{figure} \psfrag{xaxis}{$x$ } \psfrag{zaxis}{$z$ } \psfrag{x1}{$x_1$ } \ps... ...zone with index $m_3$ } {\includegraphics[width=7cm]{2831fg1.eps} } \end{figure}$ Figure 1: Geometry of the computational domain.
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In the text

$\begin{figure} {\includegraphics[width=7.4cm,clip]{2831fg2.eps} }\par\end{figure}$ Figure 2: Snapshots of the velocity field superimposed on a grey scale representation of the internal energy fluctuations (i.e. or temperature) at three different times $t=[900,\ 903,\ 906]$ . The horizontal dashed lines delimit the convection zone z=[0,1] located above the radiative zone z=[1,3].
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In the text

$\begin{figure} {\includegraphics[width=7.5cm,clip]{2831fg3.eps} } \end{figure}$ Figure 3: Normalized vertical profiles of the radiative (solid dark line), convective (dotted line) and kinetic (dashed line) fluxes, with their sum (solid grey line). The vertical dotted lines denote the CZ limits.
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In the text

$\begin{figure} {\includegraphics[width=8cm,clip]{2831fg4.eps} } \end{figure}$ Figure 4: Evolution with time of the penetration extent $\Delta$ , with its time-averaged value $\left <\Delta \right >\simeq 0.56$ denoted by the horizontal dotted line.
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In the text

$\begin{figure} {\includegraphics[width=7cm,clip]{2831fg5.eps} } \end{figure}$ Figure 5: Mean vertical profile of the Péclet number, where dotted lines mark the CZ limits.
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In the text

$\begin{figure} {\includegraphics[width=8.5cm,clip]{2831fg6.eps} } \end{figure}$ Figure 6: Left: gray scale representations in the $(z,\omega )$ -plane of the low-frequency part of the temporal power spectra for two degrees $\ell =[1,2]$ . Right: the resulting spectra after integrating over depth.
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In the text

$\begin{figure} {\includegraphics[width=6cm,clip]{2831fg7.eps} }% \end{figure}$ Figure 7: Mean vertical profile of the Brunt-Väisälä frequency N in the RZ, the dotted line denoting the BCZ.
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In the text

$\begin{figure} {\includegraphics[width=7.6cm,clip]{2831fg8.eps} } \end{figure}$ Figure 8: First three anelastic eigenvectors $\vec{\psi}_{\ell n} = (\xi_x,\xi_z)^T$ at $\ell = 1$ and radial orders n=0 (solid line), n=1 (dashed line) and n=2 (dashed-dotted line). Upper and lower panels show the vertical and horizontal displacements, respectively. Eigenvectors have been normalized by imposing $\int_{z_1}^{z_4} \rho_0 \vert\vec{\psi}_{\ell n}\vert^2\ {\rm d}z = 1$ .
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In the text

$\begin{figure} {\includegraphics[width=8.5cm,clip]{2831fg9.eps} } \end{figure}$ Figure 9: Evolution with time of the real (solid lines) and imaginary (dotted lines) parts of the amplitude $c_{\ell n}$ of the g-modes of degrees $\ell =[1,2]$ and orders $n=[0,\ 1]$ .
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In the text

$\begin{figure} {\includegraphics[width=6.7cm]{2831fg10.eps} } \end{figure}$ Figure 10: Corresponding temporal power spectrum of the mode amplitude $c_{\ell n} (t)$ used in Fig. 9, for $\ell = 1$ and n=0. The vertical dotted line marks the location of the theoretical frequency $\omega _{10}$ of the underlying g-mode. Amplitudes have been magnified by 10⁵for clarity.
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In the text

$\begin{figure} {\includegraphics[width=8cm,clip]{2831fg11.eps} }\par\end{figure}$ Figure 11: Time-frequency diagram of the amplitude of the g-mode at $\ell = 1$ and n=0 using a temporal window of width $\Delta t = 2T_{10}$ , with $T_{10}=2\pi /\omega _{10} \simeq 22.6$ the mode period. The horizontal dotted line corresponds to the mode frequency $\omega _{10}$ .
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In the text

$\begin{figure} \psfrag{toto}{Event function $\cal E$ } {\includegraphics[width=7.5cm,clip]{2831fg12.eps} }\par\end{figure}$ Figure 12: Filtering of the mode $\ell = 1$ , n=0: zoom in Fig. 11 around the frequency $\omega _{10}$ ( upper panel); the resulting event function $\cal E$ given by Eq. (12) ( middle panel); the corresponding real (solid line) and imaginary (dotted line) parts of the mode amplitude after the filtering ( lower panel).
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In the text

$\begin{figure} {\includegraphics[width=7.1cm,clip]{2831fg13.eps} }\par\end{figure}$ Figure 13: Snapshot of the velocity field superimposed on the internal energy fluctuations for time t=405. Note the large-scale velocity field in the bottom radiative zone mainly due to the standing g-mode at $\ell = 1$ and n=0.
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In the text

$\begin{figure} {\includegraphics[width=8.8cm,clip]{2831fg14.eps} } \end{figure}$ Figure 14: Destruction of the g-mode $\ell =1,\ n=0$ by a penetrating plume entering in the RZ at time $t\simeq 620$ .
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In the text

$\begin{figure} {\includegraphics[width=7.1cm,clip]{2831fg15.eps} }\par\end{figure}$ Figure 15: Upper panel: same as in Fig. 6 for $\ell = 1$ except that the temporal Fourier transform has been computed for time t=[300-450] only. Lower panel: comparison between the corresponding vertical mass flux $\widehat{\rho w}$ (solid line) and the theoretical one (dashed line) computed from the anelastic eigenvector at $\ell = 1$ and n=0.
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In the text

$\begin{figure} {\includegraphics[width=7.4cm,clip]{2831fg16.eps} } \end{figure}$ Figure 16: The event functions $\cal E$ for g-modes of degrees $\ell =[1,2,3]$ and radial orders n=[0,1,2], with their associated periods $T_{\ell n}$ .
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In the text

$\begin{figure} {\includegraphics[width=7.6cm,clip]{2831fg17.eps} }\par\end{figure}$ Figure 17: PDF of the lifetime of wave events, in units of the modeperiods.
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In the text

$\begin{figure} \par {\includegraphics[width=7.2cm,clip]{2831fg18.eps} }\par\end{figure}$ Figure 18: a) Time evolution of the total kinetic energy (solid line) embedded in the simulation, with its component which is only due to g-modes (dot-dashed line); b) ratio between the two.
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In the text

$\begin{figure} {\includegraphics[width=7.7cm]{2831fg19.eps} } \par\end{figure}$ Figure A.1: Initial vertical profiles for a layered system with m=[-0.9,-0.5,3] of the radiative conductivity a) and entropy b). The vertical dotted lines delimit the convection zone, whereas the horizontal dashed line in the a)-plot corresponds to the critical value ${\cal K}_{\hbox{\scriptsize ad}}$ below which the layer is convectively unstable. The dot-dashed line in the b)-plot corresponds to the entropy profile in the relaxed state.

In the text

$\begin{figure} \psfrag{xaxis}{$x$ } \psfrag{zaxis}{$z$ } \psfrag{x1}{$x_1$ } \ps... ...zone with index $m_3$ } {\includegraphics[width=7cm]{2831fg1.eps} } \end{figure}$	Figure 1: Geometry of the computational domain.
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$\begin{figure} {\includegraphics[width=7.4cm,clip]{2831fg2.eps} }\par\end{figure}$	Figure 2: Snapshots of the velocity field superimposed on a grey scale representation of the internal energy fluctuations (i.e. or temperature) at three different times $t=[900,\ 903,\ 906]$ . The horizontal dashed lines delimit the convection zone z=[0,1] located above the radiative zone z=[1,3].
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$\begin{figure} {\includegraphics[width=7.5cm,clip]{2831fg3.eps} } \end{figure}$	Figure 3: Normalized vertical profiles of the radiative (solid dark line), convective (dotted line) and kinetic (dashed line) fluxes, with their sum (solid grey line). The vertical dotted lines denote the CZ limits.
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$\begin{figure} {\includegraphics[width=8cm,clip]{2831fg4.eps} } \end{figure}$	Figure 4: Evolution with time of the penetration extent $\Delta$ , with its time-averaged value $\left <\Delta \right >\simeq 0.56$ denoted by the horizontal dotted line.
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$\begin{figure} {\includegraphics[width=7cm,clip]{2831fg5.eps} } \end{figure}$	Figure 5: Mean vertical profile of the Péclet number, where dotted lines mark the CZ limits.
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$\begin{figure} {\includegraphics[width=8.5cm,clip]{2831fg6.eps} } \end{figure}$	Figure 6: Left: gray scale representations in the $(z,\omega )$ -plane of the low-frequency part of the temporal power spectra for two degrees $\ell =[1,2]$ . Right: the resulting spectra after integrating over depth.
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$\begin{figure} {\includegraphics[width=6cm,clip]{2831fg7.eps} }% \end{figure}$	Figure 7: Mean vertical profile of the Brunt-Väisälä frequency N in the RZ, the dotted line denoting the BCZ.
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$\begin{figure} {\includegraphics[width=7.6cm,clip]{2831fg8.eps} } \end{figure}$	Figure 8: First three anelastic eigenvectors $\vec{\psi}_{\ell n} = (\xi_x,\xi_z)^T$ at $\ell = 1$ and radial orders n=0 (solid line), n=1 (dashed line) and n=2 (dashed-dotted line). Upper and lower panels show the vertical and horizontal displacements, respectively. Eigenvectors have been normalized by imposing $\int_{z_1}^{z_4} \rho_0 \vert\vec{\psi}_{\ell n}\vert^2\ {\rm d}z = 1$ .
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$\begin{figure} {\includegraphics[width=8.5cm,clip]{2831fg9.eps} } \end{figure}$	Figure 9: Evolution with time of the real (solid lines) and imaginary (dotted lines) parts of the amplitude $c_{\ell n}$ of the g-modes of degrees $\ell =[1,2]$ and orders $n=[0,\ 1]$ .
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$\begin{figure} {\includegraphics[width=6.7cm]{2831fg10.eps} } \end{figure}$	Figure 10: Corresponding temporal power spectrum of the mode amplitude $c_{\ell n} (t)$ used in Fig. 9, for $\ell = 1$ and n=0. The vertical dotted line marks the location of the theoretical frequency $\omega _{10}$ of the underlying g-mode. Amplitudes have been magnified by 10⁵for clarity.
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$\begin{figure} {\includegraphics[width=8cm,clip]{2831fg11.eps} }\par\end{figure}$	Figure 11: Time-frequency diagram of the amplitude of the g-mode at $\ell = 1$ and n=0 using a temporal window of width $\Delta t = 2T_{10}$ , with $T_{10}=2\pi /\omega _{10} \simeq 22.6$ the mode period. The horizontal dotted line corresponds to the mode frequency $\omega _{10}$ .
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$\begin{figure} \psfrag{toto}{Event function $\cal E$ } {\includegraphics[width=7.5cm,clip]{2831fg12.eps} }\par\end{figure}$	Figure 12: Filtering of the mode $\ell = 1$ , n=0: zoom in Fig. 11 around the frequency $\omega _{10}$ ( upper panel); the resulting event function $\cal E$ given by Eq. (12) ( middle panel); the corresponding real (solid line) and imaginary (dotted line) parts of the mode amplitude after the filtering ( lower panel).
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$\begin{figure} {\includegraphics[width=7.1cm,clip]{2831fg13.eps} }\par\end{figure}$	Figure 13: Snapshot of the velocity field superimposed on the internal energy fluctuations for time t=405. Note the large-scale velocity field in the bottom radiative zone mainly due to the standing g-mode at $\ell = 1$ and n=0.
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$\begin{figure} {\includegraphics[width=8.8cm,clip]{2831fg14.eps} } \end{figure}$	Figure 14: Destruction of the g-mode $\ell =1,\ n=0$ by a penetrating plume entering in the RZ at time $t\simeq 620$ .
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$\begin{figure} {\includegraphics[width=7.1cm,clip]{2831fg15.eps} }\par\end{figure}$	Figure 15: Upper panel: same as in Fig. 6 for $\ell = 1$ except that the temporal Fourier transform has been computed for time t=[300-450] only. Lower panel: comparison between the corresponding vertical mass flux $\widehat{\rho w}$ (solid line) and the theoretical one (dashed line) computed from the anelastic eigenvector at $\ell = 1$ and n=0.
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$\begin{figure} {\includegraphics[width=7.4cm,clip]{2831fg16.eps} } \end{figure}$	Figure 16: The event functions $\cal E$ for g-modes of degrees $\ell =[1,2,3]$ and radial orders n=[0,1,2], with their associated periods $T_{\ell n}$ .
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$\begin{figure} {\includegraphics[width=7.6cm,clip]{2831fg17.eps} }\par\end{figure}$	Figure 17: PDF of the lifetime of wave events, in units of the modeperiods.
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$\begin{figure} \par {\includegraphics[width=7.2cm,clip]{2831fg18.eps} }\par\end{figure}$	Figure 18: a) Time evolution of the total kinetic energy (solid line) embedded in the simulation, with its component which is only due to g-modes (dot-dashed line); b) ratio between the two.
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