Reexamination of the infrared properties of randomly stirred hydrodynamics

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Berera, A. and Yoffe, S. R. (2010) Reexamination of the infrared properties of randomly stirred hydrodynamics. Physical Review E, 82 (6). 066304. ISSN 2470-0053 (https://doi.org/10.1103/PhysRevE.82.066304)

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Abstract

Dynamic renormalization-group (RG) methods were originally used by Forster, Nelson, and Stephen (FNS) to study the large-scale behavior of randomly stirred incompressible fluids governed by the Navier-Stokes equations. Similar calculations using a variety of methods have been performed but have led to a discrepancy in results. In this paper, we carefully reexamine in d dimensions the approaches used to calculate the renormalized viscosity increment and, by including an additional constraint which is neglected in many procedures, conclude that the original result of FNS is correct. By explicitly using step functions to control the domain of integration, we calculate a nonzero correction caused by boundary terms which cannot be ignored. We then go on to analyze how the noise renormalization, which is absent in many approaches, contributes an O(k^2) correction to the force autocorrelation and show conditions for this to be taken as a renormalization of the noise coefficient. Following this, we discuss the applicability of this RG procedure to the calculation of the inertial range properties of fluid turbulence.

ORCID iDs

Berera, A. and Yoffe, S. R. ORCID logoORCID: https://orcid.org/0000-0002-6723-4990;
  • Item type:Article
    ID code:43584
    Dates:
    Date
    Event
    3 December 2010
    Published
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:25 Apr 2013 10:48
    Last modified:11 Nov 2024 10:23
    URI:https://strathprints.strath.ac.uk/id/eprint/43584
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