Fluid dynamics of clouds: Turbulence, coalescence, and Euler's celebrated sum

Raymond Shaw, Department of Physics Michigan Technological University

Atmospheric clouds, a crucial piece of the climate change problem, are almost iconic as visualizations of turbulence. Some of the many aspects of turbulence interacting with cloud particles and radiation fields will be reviewed: from advection-diffusion, to inertial clustering, to stochastic coalescence. A toy model of stochastic rain formation provides an unanticipated application of Euler's celebrated solution to the “Basel problem,” and this will provide a context for discussing the emerging recognition of the dominant role of fluctuations in cloud processes.