Laboratory experiments and numerical simulations have shown that volcanic ash particles immersed in water can either settle slowly and individually, or rapidly and collectively as particle-laden plumes. The ratio of timescales for individual and collective settling, in the form of analytical expressions, provides a dimensionless quantitative measure of the tendency for such plumes to grow and persist which has important implications for determining particle residence times and deposition rates. However, existing measures in the literature assume that collective settling obeys Stokes' law and is therefore controlled by the balance between gravitational forces and viscous drag, despite plume development actually being controlled by the balance between gravitational forces and inertial drag even in the absence of turbulence during early times. This paper presents a new measure for plume onset which takes into account the inertial drag-controlled (rather than viscous drag-controlled) nature of plume growth and descent. A parameter study comprising a set of numerical simulations of small-scale volcanic ash particle settling experiments highlights the effectiveness of the new measure and, by comparison with an existing measure in the literature, also demonstrates that the timescale of collective settling is grossly under-estimated when assuming that plume development is slowed by viscous drag. Furthermore, the formulation of the new measure means that the tendency for plumes to form can be estimated from the thickness and concentration of the final deposit; the magnitude and duration of particle flux across the water's surface do not need to be known. The measure therefore permits the residence times of particles in a large body of water to be more accurately and practically determined, and allows the improved interpretation of layers of volcaniclastic material deposited at the seabed
