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The Lagrangian dynamics of thermal tracer particles in Navier-Stokes fluids

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Abstract

A basic issue for Navier-Stokes (NS) fluids is their characterization in terms of the so-called NS phase-space classical dynamical system, which provides a mathematical model for the description of the dynamics of infinitesimal (or ideal) tracer particles in these fluids. The goal of this paper is to analyze the properties of a particular subset of solutions of the NS dynamical system, denoted as thermal tracer particles (TTPs), whose states are determined uniquely by the NS fluid fields. Applications concerning both deterministic and stochastic NS fluids are pointed out. In particular, in both cases it is shown that in terms of the ensemble of TTPs a statistical description of NS fluids can be formulated. In the case of stochastic fluids this feature permits to uniquely establish the corresponding Langevin and Fokker-Planck dynamics. Finally, the relationship with the customary statistical treatment of hydrodynamic turbulence (HT) is analyzed and a solution to the closure problem for the statistical description of HT is proposed.

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Authors and Affiliations

  1. Department of Mathematics and Geosciences, University of Trieste, Trieste, Italy

    Massimo Tessarotto, Claudio Asci, Alessandro Soranzo & Gino Tironi

  2. Consortium for Magnetofluid Dynamics, University of Trieste, Trieste, Italy

    Massimo Tessarotto, Claudio Cremaschini, Claudio Asci, Alessandro Soranzo, Gino Tironi & Marco Tessarotto

  3. International School for Advanced Studies (SISSA) and INFN, Trieste, Italy

    Claudio Cremaschini

  4. Civil Protection Agency, Regione Friuli Venezia-Giulia, Palmanova (Udine), Italy

    Marco Tessarotto

Authors
  1. Massimo Tessarotto
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  2. Claudio Cremaschini
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  3. Claudio Asci
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  4. Alessandro Soranzo
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  5. Gino Tironi
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  6. Marco Tessarotto
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Correspondence to Claudio Cremaschini.

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Tessarotto, M., Cremaschini, C., Asci, C. et al. The Lagrangian dynamics of thermal tracer particles in Navier-Stokes fluids. Eur. Phys. J. Plus 127, 36 (2012). https://doi.org/10.1140/epjp/i2012-12036-8

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  • DOI: https://doi.org/10.1140/epjp/i2012-12036-8

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