When do finite-size particles enhance or damp carrier turbulence?
In plain words
Particles larger than the smallest eddies, carried by a turbulent flow, can either calm the turbulence or make it stronger through the wakes they shed. No reliable rule predicts which happens.
Precise statement
For finite-size particles (diameter $d > \eta$, particle-to-fluid density ratio, volume fraction $\phi$) in homogeneous and wall-bounded turbulence, find a predictive criterion for whether carrier-phase turbulent kinetic energy increases or decreases, replacing the empirical threshold $d/L \sim 0.1$ ($L$ integral scale; Gore and Crowe 1989), and derive the magnitude of the change.
What would settle it
A theory validated by particle-resolved DNS and experiments over decades in $d/\eta$, density ratio and $\phi$.
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