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Inertial particles in turbulence: new, robust results

On the Course:   
This course started in early 2012 with the promise that it describes universal theory of behavior of small particles in turbulence that will find more and more applications with years. This promise was kept fully: in 2013 the theory was applied for clustering of living phytoplankton cells in turbulence, in 2014-2015 for water droplets sedimenting in turbulent clouds and in 2015 - for phoretic particles in the ocean. What is this theory the describes so distinct physical objects? The theory considers situation of small particles in turbulence that have a bit of their "own will": inertial particles trying keeping their velocity constant, phytoplankton in the ocean trying swimming upward toward the light and phoretic particles going down gradients of temperature, salinity or other field. These situations bring the flow of particles which differs from turbulence itself which brings the particles on fractal set in space saying that one of the defining properties of turbulence - mixing particles uniformly over the flow - is limited. If the concerned phenomena occur at fine scale, like formation of rain in warm clouds, then turbulence pushes particles to rugged fractal structure not mixing them. This clarifies by noting that random turbulent vortices repel heavy particles, like ordinary centrifuges do. The course demands only the knowledge of basics of analysis. Fractals are learnt directly by studying particles in turbulence. 
1. introduction to the problem of rain formation in warm clouds - relevance of cloud air turbulence
2. fractal distribution of small particles in turbulence - centrifuge mechanism, statistics and practical implications
(behavior of small parcels of fluid from the law of large numbers - how to predict behavior of transported particles,
not knowing the statistics of the transporting turbulent flow)
3. limitations of the concept of turbulent mixing

4. if time permits: "sling effect" where particles are pushed from rare strong vortices so violently that their contribution to the overall collision rate of particles is significant; phytoplankton patchiness .                                                                            Lecture notes

This course was given

Nagoya Institute of Technology, Nagoya, Japan, on 6 February - 10 February, 2012.                                watch video

Inaugural Center for Environmental & Applied Fluid Mechanics Short Course, John Hopkins University, Baltimore, USA, 9-12 September, 2013.

Niels Bohr Institute, Copenhagen, Denmark, on 23 September - 26 September, 2013.     recommendation letter 

KTH, Stockholm, Sweden, on 28 October - 31 October, 2013.

Yonsei University, Seoul, South Korea, on February 4 - February 6, 2014.

CISM, Udine, Italy, within the school "Collective Dynamics of Particles: from Viscous to Turbulent Flows", May 30 2014.

ETH, Zürich, Switzerland, June 10 - June 11, 2014.

Vilnius State University, Vilnius, Lithuania, October 17 - October 21, 2014. 

Center for Compressible Multiphase Turbulence, University of Florida, USA, December 8 - December 11, 2014. 

Environmental Research Laboratory, Institute of Nuclear Technology and Radiation Protection, NCSR Demokritos, Athens, Greece December 16, 2014. 

Institute of Cybernetics, Tallinn University of Technology, Estonia, November 27 - November 28, 2015. 

School of Earth and Environmental Sciences, Seoul National University, South Korea, June 2 - June 8, 2016. 

Basic references:
G. Falkovich, A. Fouxon and M. Stepanov, Acceleration of rain initiation by cloud turbulence, Nature 419, 151-154 (2002). 
It is demonstrated that small water droplets in warm clouds form fractals due to turbulence. Sling effect of swirls-induced collisions is discovered. This increases the rate of formation of rain.                                                             Read

I. Fouxon, Distribution of particles and bubbles in turbulence at small Stokes number, Phys. Rev. Lett. 108, 134502 (2012).
Complete description of the fractal distribution of particles in turbulence is provided.                                  Read

I. Fouxon, Y. Park, R. Harduf, and C. Lee, Inhomogeneous distribution of water droplets in cloud turbulence, Phys. Rev. E 92, 033001 (2015).                                                                                                                                                           Read
Statistics of spatial distribution of inertial particles sedimenting in Navier-Stokes turbulence is derived in terms of the energy spectrum and confirmed numerically. 

I. Fouxon and A. Leshansky, Phytoplankton’s motion in turbulent ocean, Phys. Rev.  E 92, 013017 (2015).    Read
Criterion for disorientation of phytoplankton by turbulence is derived. Fractal concentration is predicted in new range of parameters.

L. Schmidt, I. Fouxon, D. Krug, M. van Reeuwijk and M. Holzner, Clustering of particles in turbulence due to phoresis, Phys. Rev. E 93, 063110 (2016).
It is demonsrated that phoresis in turbulence brings preferential concentration. It is conjectured that this preferential concentration accelerates formation of marine snow (composed by organic sediments) in the ocean.            Read

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