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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{6899fig1} \end{figure}$ Figure 1: The function $\frac{2}{3}y^*(y^*-1)^2 - 1/(1+y^*)$ . If $t_{\rm s} \ll t_{\rm L}$ and $V_{\rm o}=0$ (no systematic velocity drifts; see Sect. 3.3) this equation is equal to zero and we find a solution $y^* = t^*/t_{\rm s} \approx y_{\rm a}^* = 1.6$ . On the other hand, for $t_{\rm s} \sim t_{\rm L}$ , the RHS of Eq. (24) is $\approx$ -0.5 and $y^* \approx 1$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6899fig2} \end{figure}$ Figure 2: Three different assumptions for t^* (or the related k^*) are shown here.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{6899fig3} \end{figure}$ Figure 3: Exact solution to Eq. (16) for $\Delta V_{12}$ in the case of identical particles (dashed line) and $t_1 \gg t_2$ (solid line) for a Reynold number of 10⁸. The dotted curves are approximations to Eq. (16) given by Eqs. (27)-(29).
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In the text

$\begin{figure} \par\includegraphics[width=12.6cm,clip]{6899fig4} \end{figure}$ Figure 4: Contour plots of particle-particle, turbulence induced, relative velocities $\Delta V_{12}$ normalized to $V_{\rm g}$ . A) Numerical results of Markiewicz et al. (1991), without inner scale ( ${\rm Re}\rightarrow \infty$ ). B) Analogous result from our closed-form expressions with the fixed $y^* \approx y^*_{\rm a} = 1.6$ approximation (Sect. 3.2.1). C) Like B, but with an exact solution for y^* and with ${\rm Re}=10^8$ . D) Using the CH03 formula for k^*, $k^*/k_L = 0.5{\rm St}^* + 1$ , and also with ${\rm Re}=10^8$ . Contours are drawn twice per logarithmic decade (at $\Delta V_{12}/V_{\rm g} = 3\times 10^i$ and at 10ⁱ) with an additional contour at 0.8 and 1.15.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6899figA} \end{figure}$ Figure A.1: The functions g (solid lines) and h (dashed lines) plotted for three different Stokes numbers at a Reynolds number of 10⁸. After k>k^* the functions show power-law behavior. The power spectrum (weighted by k) is plotted by the dotted line.

In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{6899fig1} \end{figure}$	Figure 1: The function $\frac{2}{3}y^(y^-1)^2 - 1/(1+y^)$ . If $t_{\rm s} \ll t_{\rm L}$ and $V_{\rm o}=0$ (no systematic velocity drifts; see Sect. 3.3) this equation is equal to zero and we find a solution $y^ = t^/t_{\rm s} \approx y_{\rm a}^ = 1.6$ . On the other hand, for $t_{\rm s} \sim t_{\rm L}$ , the RHS of Eq. (24) is $\approx$ -0.5 and $y^* \approx 1$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{6899fig2} \end{figure}$	Figure 2: Three different assumptions for t^* (or the related k^*) are shown here.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{6899fig3} \end{figure}$	Figure 3: Exact solution to Eq. (16) for $\Delta V_{12}$ in the case of identical particles (dashed line) and $t_1 \gg t_2$ (solid line) for a Reynold number of 10⁸. The dotted curves are approximations to Eq. (16) given by Eqs. (27)-(29).
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