The Influence of Particle Concentration on the Formation of Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds

Abstract

<jats:p>Settling-driven gravitational instabilities observed at the base of volcanic ash clouds have the potential to play a substantial role in volcanic ash sedimentation. They originate from a narrow, gravitationally unstable region called a Particle Boundary Layer (PBL) that forms at the lower cloud-atmosphere interface and generates downward-moving ash fingers that enhance the ash sedimentation rate. We use scaled laboratory experiments in combination with particle imaging and Planar Laser Induced Fluorescence (PLIF) techniques to investigate the effect of particle concentration on PBL and finger formation. Results show that, as particles settle across an initial density interface and are incorporated within the dense underlying fluid, the PBL grows below the interface as a narrow region of small excess density. This detaches upon reaching a critical thickness, that scales with <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>ν</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math></jats:inline-formula>, where <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mi>ν</mml:mi></mml:math></jats:inline-formula> is the kinematic viscosity and <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:msup><mml:mi>g</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math></jats:inline-formula> is the reduced gravity of the PBL, leading to the formation of fingers. During this process, the fluid above and below the interface remains poorly mixed, with only small quantities of the upper fluid phase being injected through fingers. In addition, our measurements confirm previous findings over a wider set of initial conditions that show that both the number of fingers and their velocity increase with particle concentration. We also quantify how the vertical particle mass flux below the particle suspension evolves with time and with the particle concentration. Finally, we identify a dimensionless number that depends on the measurable cloud mass-loading and thickness, which can be used to assess the potential for settling-driven gravitational instabilities to form. Our results suggest that fingers from volcanic clouds characterised by high ash concentrations not only are more likely to develop, but they are also expected to form more quickly and propagate at higher velocities than fingers associated with ash-poor clouds.</jats:p>