All Figures

$\begin{figure} \par\includegraphics[width=5.9cm,clip]{0391f1a.eps}\hspace*{5mm} ... ...c.eps}\hspace*{5mm} \includegraphics[width=5.7cm,clip]{0391f1d.eps} \end{figure}$ Figure 1: a) A contour plot of the z component of the perturbed velocity, v_z, at t=20.2, with $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . b) Corresponding contour plot of the x component of the perturbed velocity, v_x. c)- d) Similar to a) and b) but surface plots. Note the difference in the horizontal and vertical scales in these figures.
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In the text

$\begin{figure} \par\includegraphics[width=6.1cm,clip]{0391f2a.eps}\hspace*{3mm} ... ...e.eps}\hspace*{3mm} \includegraphics[width=6.1cm,clip]{0391f2f.eps} \end{figure}$ Figure 2: a) A cross-section of the z component of the perturbed velocity, v_z, at x=0.25 and t=20.2, with $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . b)- c) Similar to a) but at x=0.5 and x=0.75, respectively. d)- f) Corresponding cross-sections of the x component of the perturbed velocity, v_x.
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In the text

$\begin{figure} \par\includegraphics[width=5.8cm,clip]{0391f3a.eps}\hspace*{3mm} ... ...f3c.eps}\hspace*{3mm} \includegraphics[width=6cm,clip]{0391f3d.eps} \end{figure}$ Figure 3: a) A contour plot of the z component of the perturbed velocity, v_z, at t=38.2, with $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =\pi$ . b) Corresponding contour plot of the x component of the perturbed velocity, v_x. c)- d) Cross-sections at x=0.5 of the z component and x component, respectively. The dot-dashed lines correspond to analytical approximations which will be discussed in Sect. 4.3.
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0391f4a.eps}\hspace*{4mm} \includegraphics[width=6.4cm,clip]{0391f4b.eps} \end{figure}$ Figure 4: a) A cross-section of the z component of the perturbed velocity, v_z, at x=0.5 and t=90.2, with $\varepsilon =0.5$ , $\beta =0.01$ and $\omega =\pi$ . b) Corresponding cross-sections of the x component of the perturbed velocity, v_x. The dot-dashed lines correspond to analytical approximations which will be discussed in Sect. 4.3.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0391f5a.eps}\hspace*{3mm} \includegraphics[width=7cm,clip]{0391f5b.eps} \end{figure}$ Figure 5: a) A cross-section of the z component of the perturbed velocity at x=0.5 and t=21.6, with $\nu =0.001$ , $\varepsilon =0.1$ , $\beta =0.1$ and $\omega =\pi$ . The dot-dashed line corresponds to the predicted damping rate (Eq. (10)). The dashed line corresponds to the predicted damping rate for $\varepsilon =0$ . (Eq. (11)) b) Similar to a) but with $\varepsilon =0.5$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{0391f6a.eps}\hspace*{3mm} \includegraphics[width=5.8cm,clip]{0391f6b.eps} \end{figure}$ Figure 6: a) A cross-section of the x component of the perturbed velocity at x=0.5 and t=50.2, with $\varepsilon =0.5$ (solid line) and $\varepsilon =0.1$ (dashed line), $\beta =0.01$ and $\omega =\pi$ . The dot-dashed and long-dashed lines are the corresponding analytical approximations. b) The behaviour of k/k^' as a function of $\varepsilon$ . The dotted lines indicate the location of the maximum of A for $\varepsilon$ equal to 0.1 and 0.5, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=5.8cm,clip]{0391f7a.eps}\hspace*{3mm} \includegraphics[width=6cm,clip]{0391f7b.eps} \end{figure}$ Figure 7: a) The variation of the (squares of) the fast (solid line) and slow (dashed line) wavenumber, given by Eq. (33), as a function of the driving frequency $\omega$ and with $\beta =0.1$ . The dotted lines indicate $\omega =\pi$ and $\omega =2\pi$ . b) The variation of the (square of) the fast wavenumber, given by Eq. (33), as a function of $\beta$ and with $\omega =\pi$ and with $\beta =0.1$ . The symbols correspond to the values obtained for the fast wavenumber in Sect. 4.3, with $\varepsilon =0.5$ (plus), $\varepsilon =0.1$ (diamond) and $\varepsilon =0.05$ (star).
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In the text

$\begin{figure} \par\includegraphics[width=5.8cm,clip]{0391f8a.eps}\hspace*{2mm} \includegraphics[width=5.9cm,clip]{0391f8b.eps} \end{figure}$ Figure 8: a) A normalised cross-section (at constant height) of the x component of the fundamental fast (solid) and slow (dashed) modes. b) Profiles of $\omega / v_{\rm A}$ , $\omega / c_{\rm s}$ and $\omega / c_{\rm T}$ for $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . The long-dashed lines correspond to the fundamental fast and slow mode wavenumbers.
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In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{0391f9a.eps}\hspace*{2mm} \includegraphics[width=6.1cm,clip]{0391f9b.eps} \end{figure}$ Figure 9: a) A cross-section of the x component of the perturbed velocity at x=0.75 and t=20.2, with $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . The dot-dashed line corresponds to the normal slow mode, whereas the long-dashed line is the normal fast mode. b) The same cross-section of v_x. The dashed line is obtained by adding the appropriate small $\beta$ expansion and the normal modes.
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In the text

$\begin{figure} \par\includegraphics[width=5.9cm,clip]{0391f1a.eps}\hspace{5mm} ... ...c.eps}\hspace{5mm} \includegraphics[width=5.7cm,clip]{0391f1d.eps} \end{figure}$	Figure 1: a) A contour plot of the z component of the perturbed velocity, v_z, at t=20.2, with $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . b) Corresponding contour plot of the x component of the perturbed velocity, v_x. c)- d) Similar to a) and b) but surface plots. Note the difference in the horizontal and vertical scales in these figures.
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$\begin{figure} \par\includegraphics[width=6.1cm,clip]{0391f2a.eps}\hspace{3mm} ... ...e.eps}\hspace{3mm} \includegraphics[width=6.1cm,clip]{0391f2f.eps} \end{figure}$	Figure 2: a) A cross-section of the z component of the perturbed velocity, v_z, at x=0.25 and t=20.2, with $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . b)- c) Similar to a) but at x=0.5 and x=0.75, respectively. d)- f) Corresponding cross-sections of the x component of the perturbed velocity, v_x.
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0391f4a.eps}\hspace*{4mm} \includegraphics[width=6.4cm,clip]{0391f4b.eps} \end{figure}$	Figure 4: a) A cross-section of the z component of the perturbed velocity, v_z, at x=0.5 and t=90.2, with $\varepsilon =0.5$ , $\beta =0.01$ and $\omega =\pi$ . b) Corresponding cross-sections of the x component of the perturbed velocity, v_x. The dot-dashed lines correspond to analytical approximations which will be discussed in Sect. 4.3.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0391f5a.eps}\hspace*{3mm} \includegraphics[width=7cm,clip]{0391f5b.eps} \end{figure}$	Figure 5: a) A cross-section of the z component of the perturbed velocity at x=0.5 and t=21.6, with $\nu =0.001$ , $\varepsilon =0.1$ , $\beta =0.1$ and $\omega =\pi$ . The dot-dashed line corresponds to the predicted damping rate (Eq. (10)). The dashed line corresponds to the predicted damping rate for $\varepsilon =0$ . (Eq. (11)) b) Similar to a) but with $\varepsilon =0.5$ .
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$\begin{figure} \par\includegraphics[width=5.8cm,clip]{0391f8a.eps}\hspace*{2mm} \includegraphics[width=5.9cm,clip]{0391f8b.eps} \end{figure}$	Figure 8: a) A normalised cross-section (at constant height) of the x component of the fundamental fast (solid) and slow (dashed) modes. b) Profiles of $\omega / v_{\rm A}$ , $\omega / c_{\rm s}$ and $\omega / c_{\rm T}$ for $\varepsilon =0.5$ , $\beta =0.1$ and $\omega =2\pi$ . The long-dashed lines correspond to the fundamental fast and slow mode wavenumbers.
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