# Development of Attached Cavitation at Very Low Reynolds Numbers from Partial to Super-Cavitation
## 3 Results
### Quantitative Characterization of the Different Regimes and Effects of the Reynolds Number
The experiments are plotted in this parameter space in Figure 11. The points at constant Reynolds number are plotted with the same symbol. The development of cavitation associated with a decrease of the ambient pressure corresponds to a path from top right to bottom left in this parameter space. For the seven Reynolds numbers that are displayed in the Figure 11, one can first notice that the points follow a similar trend: the two pressures are decreasing together. Moreover, one can distinguish two main different shapes in the curves. On the one hand, for \(Re\simeq 1000\) and \(Re\simeq 1200\), the points align quite on a straight path. On the other hand, for \(Re\geqslant 1300\), one can notice some kind of break in the slope of the curve around \(\sigma_{2}\simeq 1\). For \(\sigma_{2}\geqslant 1\), the slope is of the order of magnitude of the former (roughly \(-2\)), whereas for \(\sigma_{2}\leqslant 1\), the slope is steeper, of the order of \(-10\): a very small decrease in the inlet pressure causes a  
Figure 10: Dimensionless average length of the attached cavity \(L^{*}\) as a function of the outlet cavitation number \(\sigma_{2}\). For \(Re\geqslant 1300\), the symbols refer to the regimes identified in Figure 6: type-1 steady cavity (\(\bullet\)), type-2 cavity with periodic shrinking (\(\blacksquare\)), type-3 unsteady cavity with no clear periodic behavior (\(\times\)) and type-4 supercavity (\(\blacklozenge\)). The lines are a guide to the eye based on spline interpolation of the points at \(Re=800\), \(Re=1000\), \(Re=1200\) and of all the points for \(Re\geqslant 1400\). Figure 9: Measured frequency as a function of the throat velocity for type-2 regime. The dashed line is a linear fit of equation \(f=3.83V_{throat}\). dramatic decrease of the outlet pressure corresponding to the fast increase of the cavity length observed in Figure 10.  
These observations support the idea of a transition in the cavitating flow that takes place around \(Re\simeq 1300\). Looking at the attached cavities from top (see the right column in Figures 2, 5 and 7), one can notice that the morphology of the cavity also exhibits a dependence in the transverse direction \(Y^{*}\). At very low Reynolds number (see Figure 7a) the interface at the leading edge presents a single smooth and convex cap. At larger Reynolds numbers (see Figure 7d) this interface presents several indentations. These structures resemble the \"divots\" that have been discussed for instance in Ref. [35] and that are attributed to a local breakdown of the two-dimensionality of the laminar boundary layer. We report in Figure 12 the number of indentations that are observed on the cavities of an average length of \(L^{*}\geqslant 4\). The first indentation is observed at \(Re\simeq 1200\) and then their number increases almost linearly with the Reynolds number. Figure 11: Explored map in the inlet cavitation number—outlet cavitation number (\(\sigma_{1}-\sigma_{2}\)). The different symbols stand for different Reynolds numbers. The arrows are guides to the eye. Figure 12: Number of transverse indentations at the leading edge of the developed attached cavities as a function of the Reynolds number.