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Field and matrix models of two-dimen...

Mayo, Jackson Ralph.

Field and matrix models of two-dimensional turbulence.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Field and matrix models of two-dimensional turbulence.
Author:	Mayo, Jackson Ralph.
Description:	112 p.
Notes:	Adviser: Alexander M. Polyakov.
Notes:	Source: Dissertation Abstracts International, Volume: 66-06, Section: B, page: 3199.
Contained By:	Dissertation Abstracts International66-06B.
Subject:	Physics, Fluid and Plasma.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3180066
ISBN:	9780542198069

Field and matrix models of two-dimensional turbulence.
Mayo, Jackson Ralph.

Field and matrix models of two-dimensional turbulence. - 112 p.

Adviser: Alexander M. Polyakov.

Thesis (Ph.D.)--Princeton University, 2005.

The turbulent behavior of a two-dimensional incompressible fluid is interesting for its atmospheric and astrophysical applications as well as for its unique dynamical features. In contrast to the three-dimensional case, energy injected by continual stirring is transferred to ever-larger scales in an "inverse cascade." Linear friction (rather than viscosity) can ultimately dissipate the energy, resulting in statistically stationary turbulence. This large-scale behavior is analyzed here using the path-integral form of stochastic dynamics and the renormalization-group (RG) methods of quantum field theory. Galilean invariance and the fluctuation-dissipation theorem (FDT) reflect important symmetries of the path integral and together imply vanishing anomalous dimensions. Thus the observed nontrivial scaling of the inverse cascade cannot be explained by any RG fixed point. Instead, the scaling is conjectured to arise from a linear beta function at strong coupling, consistent with an extrapolation of the two-loop perturbative beta function. The RG flow indicates violation of scale invariance, but the expected intermittency has not been definitively observed. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade---in agreement with numerical simulations. For a complementary view of the two-dimensional inverse cascade, a discrete-time matrix model is used to compactify the configuration space of a fluid two-sphere and enable a strong-coupling expansion. At infinite coupling, the fluid configuration is uncorrelated in time and the energy stays at small scales. The leading correction, however, suggests a continuous-time limit qualitatively consistent with the inverse cascade.

ISBN: 9780542198069Subjects--Topical Terms:

227264
Physics, Fluid and Plasma.

Field and matrix models of two-dimensional turbulence.
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502 $a Thesis (Ph.D.)--Princeton University, 2005.
520 # $a The turbulent behavior of a two-dimensional incompressible fluid is interesting for its atmospheric and astrophysical applications as well as for its unique dynamical features. In contrast to the three-dimensional case, energy injected by continual stirring is transferred to ever-larger scales in an "inverse cascade." Linear friction (rather than viscosity) can ultimately dissipate the energy, resulting in statistically stationary turbulence. This large-scale behavior is analyzed here using the path-integral form of stochastic dynamics and the renormalization-group (RG) methods of quantum field theory. Galilean invariance and the fluctuation-dissipation theorem (FDT) reflect important symmetries of the path integral and together imply vanishing anomalous dimensions. Thus the observed nontrivial scaling of the inverse cascade cannot be explained by any RG fixed point. Instead, the scaling is conjectured to arise from a linear beta function at strong coupling, consistent with an extrapolation of the two-loop perturbative beta function. The RG flow indicates violation of scale invariance, but the expected intermittency has not been definitively observed. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade---in agreement with numerical simulations. For a complementary view of the two-dimensional inverse cascade, a discrete-time matrix model is used to compactify the configuration space of a fluid two-sphere and enable a strong-coupling expansion. At infinite coupling, the fluid configuration is uncorrelated in time and the energy stays at small scales. The leading correction, however, suggests a continuous-time limit qualitatively consistent with the inverse cascade.
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