The transmission dynamics of highly contagious respiratory diseases like COVID-19 (through coughing/sneezing) is an open problem in the epidemiological studies of such diseases (Bourouiba, JAMA. https ://doi.org/10.1001/jama.2020.4756. 2020). The problem is basically the fluid dynamics of a transient turbulent jet/puff with buoyancy, laden with evaporating droplets carrying the pathogen. A turbulent flow of this nature does not lend itself to reliable estimates through modeling approaches such as RANS (Reynolds-Averaged Navier-Stokes equations) or other droplet-based models. However, direct numerical simulations (DNS) of what may be called "cough/sneeze flows" can play an important role in understanding the spread of the contagion. The objective of this work is to develop a DNS code for studying cough/sneeze flows by a suitable combination of the DNS codes available with the authors (developed to study cumulus cloud flows including thermodynamics of phase change and the dynamics of small water droplets) and to generate useful data on these flows. Recent results from the cumulus cloud simulations are included to highlight the effect of turbulent entrainment (which is one of the key processes in determining the spread of the expiratory flows) on the distribution of liquid water content in a moist plume. Furthermore, preliminary results on the temperature distribution in a "dry cough" (i.e., without inclusion of liquid droplets) are reported to illustrate the large spatial extent and time duration over which the cough flow can persist after the coughing has stopped. We believe that simulations of this kind can help to devise more accurate guidelines for separation distances between neighbors in a group, design better masks, and minimize the spread of respiratory diseases of the COVID-19 type.

We study the formation of caustics in vortex-dominated flows. We find that only particles starting within a critical distance of a vortex which scales as the square roots of the particle inertia and the circulation can form sling caustics. We show that particles starting in an annular region around this critical radius contribute the densest clusters in the flow. The large density spikes occurring for such particles, even at small inertia, are indicative that these particles will experience large collision rates.

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We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices.In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable frame-fixed points exist only for particle Stokes number St < St cr .We estimate St cr and compare this with direct numerical simulations, and find that the addition of viscosity increases the St cr slightly. We also find that the fixed points become more stable with increasing St until they abruptly disappear at St = St cr . These frame-fixed points are between fixed points and limit cycles in character.