All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{2695fig1.eps}\end{figure}$ Figure 1: Schematic view of the modelled subsurface spherical shell (in plain slab geometry). The dashed horizontal lines schematically represent the boundaries of the thin layers considered in our multi-layer model. Within each of these thin layers the sound speed is assumed to be approximately constant corresponding to the piecewise constant temperature profiles shown in Figs. 3 or 7.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2695fig2.eps} \end{figure}$ Figure 2: Schematic view of the piecewise straight ray path.
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In the text

$\begin{figure} \par\includegraphics[width=16.3cm,clip]{2695fig3.eps} \end{figure}$ Figure 3: Piecewise constant radial profile of the temperature (panel A) and scale height (panel B) corresponding to the case of the simple velocity profile addressed in Sect. 3.2.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{2695fig4.eps} \end{figure}$ Figure 4: The variation of the modal frequency in time. The curves correspond to the mode $\ell =951$ , n=2 and with the basic modal frequency $\nu _0 =4.5243$ mHz. The calculations have been done for a simple, linear profile of the flow velocity with the shear parameters equal to a=-1 $\times$ 10^-6 s^-1, b=2.5 $\times$ 10^-5 s^-1 and c=2.0 $\times$ 10^-5 s^-1. Panel A: curve a corresponds to k_y0>0 (angle $\beta = 45^{\circ }$ ) and curve b corresponds to k_y0<0 (angle $\beta = -45^{\circ }$ ). The points denoted by 1a and 1b correspond to the frequency of the respective mode close to its upper turning points (i.e. the frequencies observable on the surface!) while the inner turning points are denoted by 2a and 2b. Panel B: curves of the frequency variation corresponding to the upper turning points for different directions of the horizontal wavevector k_h (i.e. for different values of the angle $\beta$ ). The curves are denoted respectively as: a₁ and a₂ - $\beta = \pm 5^{\circ }$ (crossed lines), b₁ and b₂ - $\beta = \pm 30^{\circ }$ (dashed lines), c₁ and c₂ - $\beta = \pm 45^{\circ }$ (solid lines), d₁ and d₂ - $\beta = \pm 60^{\circ }$ (dotted lines), e₁ and e₂ - $\beta = \pm 85^{\circ }$ (dash-dotted lines).
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2695fig5.eps} \end{figure}$ Figure 5: Results of the calculations for the same mode as in Fig. 4 for a smaller value of the shear parameter a=-0.1 $\times$ 10^-6 s^-1. The value of the shear parameter b has been taken the same as in Fig. 4 (b=2.5 $\times$ 10^-5 s^-1). In panel A we show the curve of the frequency variation in time, for the angle $\beta = 45^{\circ }$ , within the first three evolution hours. The solid line corresponds to c=2.0 $\times$ 10^-5 s^-1 and the dashed line to c=3.0 $\times$ 10^-5 s^-1. Similar curves are plotted in panel B for the angle $\beta =30^{\circ }$ , where the dashed-dotted line corresponds to the smaller value of the parameter c and the dotted line to the larger one. Panel C shows the resulting modal frequency evolution over a time interval of 10 h. The different line styles correspond to the line styles in the previous panels.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{2695fig6.eps}\end{figure}$ Figure 6: Profile of the rotational velocity in the solar subsurface layers. The solid line shows the sample profile for latitude angle $15^{\circ }$ given by González Hernández & Patrón (2000). The dotted curve is the observed rotational profile. The solid lines show the modelled linear approximations of the observed profile for different fractional radii.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2695fig7.eps} \end{figure}$ Figure 7: As in Fig. 3 corresponding to the range of the fractional radius values r=0.95-1.00. The squares in the right bottom corners show the areas plotted in respective panels of Fig. 3.
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In the text

$\begin{figure} \par\includegraphics[width=12.8cm,clip]{2695fig8.eps} \end{figure}$ Figure 8: The variation of the modal frequencies in time calculated in the case of the velocity shear profile described in Sect. 4.1 (see Table 1). The direction of the horizontal wavevector is taken as $\beta = \pm 45^{\circ }$ . Curves a₁ and a₂ (dashed lines) correspond to the sample mode with $\ell =95$ , n=4 and with basic modal frequency $\nu _0=2.3761$ mHz. Similarly, the b₁-b₂(dashed dotted lines) and c₁-c₂ (dotted lines) respectively are curves for the modes $\ell =263$ , n=6, $\nu _0=4.2336$ mHz and $\ell =673$ , n=2, $\nu _0=3.8202$ mHz. The curves d₁-d₂(solid lines) correspond to the same mode with $\ell =951$ considered in Sect. 3.2. Different panels show results of calculations in the three different cases of the latitudinal gradient of the rotational velocity: panel A) the parameter a=-1 $\times$ 10^-8 s^-1; panel B) a=-1 $\times$ 10^-7 s^-1; panel C) a=-3 $\times$ 10^-7 s^-1; panel D) a=-6 $\times$ 10^-7 s^-1; panel E) a=-1 $\times$ 10^-6 s^-1. Note that the ordinate axes in panels A)- E) have different scales. In panel F) the frequency residuals arising after a 10 h period are plotted as functions of the shear parameter |a|absolute values.
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2695fig9.eps} \end{figure}$ Figure 9: Schematic view of the peak(s) in the power spectrum corresponding to the oscillation mode with a given angular degree. a) In static medium; b) in the case of uniform flow; c) inhomogeneous flow without the non-modal effects; d) inhomogeneous flow including the non-modal effects.
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In the text

$\begin{figure} \par\includegraphics[width=13.4cm,clip]{2695fig10.eps} \end{figure}$ Figure 10: Schematic view of the modal ray paths: A) without non-modal effects; B) same as panel A (solid line) and the non-modal deformation of the ray path due to the temporal evolution of the radial component k_z of the wavevector, which first increases and then decreases in length (dashed line) and vice versa (dash-dotted lines); C) the non-modal deformation of the ray path because of the temporal evolution of the meridional component k_y of the wavevector (dashed and dash-dotted lines). The modes do not stay in one plane; the trajectories become 3D curves.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{2695fig1.eps}\end{figure}$	Figure 1: Schematic view of the modelled subsurface spherical shell (in plain slab geometry). The dashed horizontal lines schematically represent the boundaries of the thin layers considered in our multi-layer model. Within each of these thin layers the sound speed is assumed to be approximately constant corresponding to the piecewise constant temperature profiles shown in Figs. 3 or 7.
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2695fig2.eps} \end{figure}$	Figure 2: Schematic view of the piecewise straight ray path.
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$\begin{figure} \par\includegraphics[width=16.3cm,clip]{2695fig3.eps} \end{figure}$	Figure 3: Piecewise constant radial profile of the temperature (panel A) and scale height (panel B) corresponding to the case of the simple velocity profile addressed in Sect. 3.2.
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{2695fig6.eps}\end{figure}$	Figure 6: Profile of the rotational velocity in the solar subsurface layers. The solid line shows the sample profile for latitude angle $15^{\circ }$ given by González Hernández & Patrón (2000). The dotted curve is the observed rotational profile. The solid lines show the modelled linear approximations of the observed profile for different fractional radii.
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2695fig7.eps} \end{figure}$	Figure 7: As in Fig. 3 corresponding to the range of the fractional radius values r=0.95-1.00. The squares in the right bottom corners show the areas plotted in respective panels of Fig. 3.
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$\begin{figure} \par\includegraphics[width=11cm,clip]{2695fig9.eps} \end{figure}$	Figure 9: Schematic view of the peak(s) in the power spectrum corresponding to the oscillation mode with a given angular degree. a) In static medium; b) in the case of uniform flow; c) inhomogeneous flow without the non-modal effects; d) inhomogeneous flow including the non-modal effects.
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