Predicting cavitation inception from turbulent vortex statistics and nuclei content
In plain words
In fast water flow, the first bubbles appear inside short-lived whirlpools where the pressure drops below the vapor pressure, but only if tiny gas seeds (nuclei) are present. Predicting the flow speed at which this starts requires knowing how deep the pressure dips get and how long seeds stay inside them.
Precise statement
For a turbulent shear layer, wake or tip vortex in water with nuclei size distribution $n(R)$, predict the inception cavitation number $\sigma_i = (p_{\mathrm{inf}} - p_v)/(\rho U^2/2)$ as a function of Reynolds number Re and $n(R)$, including the empirical power laws $\sigma_i \sim \mathrm{Re}^a$ ($a$ near 0.4 for tip vortices). An answer combines the statistics of pressure minima and their lifetimes in turbulent vortices with the dynamic response of nuclei (Blake critical pressure, residence time) and is validated across model and full scale.
What would settle it
Simultaneous measurement of nuclei distributions, pressure-minimum statistics and inception events in a water tunnel at several scales, matched by a predictive theory without scale-specific fitting.