Solution (source code)

= Solution

A large gas volume can reduce the effective <mass density> of the water surrounding the hull. In the simple quasihydrostatic model for the <buoyancy of an aerated liquid>, gas <void fraction> $\alpha$ gives
$$
\rho_{\rm mix}=(1-\alpha)\rho_w+\alpha\rho_g\simeq(1-\alpha)\rho_w.
$$
By <Archimedes' principle>, a boat displacing volume $V_{\rm disp}$ then has <buoyant force> $\rho_{\rm mix}gV_{\rm disp}$. To support the same boat mass $m$, it needs a larger displaced volume $m/\rho_{\rm mix}$, so its draft increases. If that exceeds the available watertight displacement, it can lose flotation or become swamped:
$$
\boxed{\rho_{\rm mix}V_{\max}<m\quad\Longrightarrow\quad
\text{insufficient hydrostatic buoyancy}.}
$$
Uneven aeration and strong plume motion can also disturb stability. This explains a possible hazard, not a claim that any bubble plume must sink a boat: upward water flow, turbulence and the distribution of bubbles can exert substantial additional forces.