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Caustics in turbulent aerosols: an excitable system approach

Barta, Robin and Vollmer, Jürgen (2022) Caustics in turbulent aerosols: an excitable system approach. Journal of Fluid Mechanics, 949 (A36), pp. 1-23. Cambridge University Press. doi: 10.1017/jfm.2022.767. ISSN 0022-1120.

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Official URL: https://doi.org/10.1017/jfm.2022.767


Aerosol particles are inertial particles. They cannot follow the surrounding fluid in a region of high vorticity. These encounters render the particle velocity field v locally compressible. Caustics occur if the trace of the gradient matrix \sigma of the field v locally diverges. For three-dimensional isotropic and homogeneous turbulence, the dynamics of the gradient matrix can be expressed in terms of three geometric invariants. In the present paper we establish a parametrisation of this problem where the dynamics takes the form of an excitable stochastic dynamical system with a three-dimensional phase space. The deterministic part of the dynamics is solved analytically. We show that the deterministic system has a globally attractive stable fixed point. Small noise induces excursions from the fixed point that typically relax straight back towards the fixed point. Caustics emerge as non-trivial return to a global fixed point when noise excites a trajectory across a stability threshold. The relaxation to the global fixed point will then involve at least one, and it may involve two or even three divergences of Tr \sigma. Based on a combination of analytical insights and numerical analysis, we determine the rate of occurrence, duration and relative observation probability of caustic events in turbulent aerosols. Our analysis reveals that each approach towards a divergence proceeds along a straight line in the phase space of the dynamical system, which can help identify caustics. Moreover, there are infinite ways in which caustics can arise, namely whenever Tr \sigma tends to negative infinity, so that no two caustics look the same.

Item URL in elib:https://elib.dlr.de/188642/
Document Type:Article
Title:Caustics in turbulent aerosols: an excitable system approach
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Barta, RobinUNSPECIFIEDhttps://orcid.org/0000-0001-8882-5864UNSPECIFIED
Vollmer, JürgenUni Leipzighttps://orcid.org/0000-0002-8135-1544UNSPECIFIED
Date:25 October 2022
Journal or Publication Title:Journal of Fluid Mechanics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 1-23
EditorsEmailEditor's ORCID iDORCID Put Code
Publisher:Cambridge University Press
Keywords:aerosols/atomisation, isotropic turbulence , excitable systems
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Transport
HGF - Program Themes:Rail Transport
DLR - Research area:Transport
DLR - Program:V SC Schienenverkehr
DLR - Research theme (Project):V - RoSto - Rolling Stock
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Ground Vehicles
Deposited By: Barta, Robin
Deposited On:18 Oct 2022 15:06
Last Modified:21 Sep 2023 12:46

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