Critical points in two-dimensional stationary homogeneous isotropic turbulence
Author(s)
Faber, Tristan Friedrich
Type
Thesis
Abstract
Basic properties of critical points in two dimensions are reviewed and related to the
velocity and acceleration field of two-dimensional turbulence. A direct numerical simulation
(DNS) of two-dimensional homogeneous isotropic turbulence with an inverse energy
cascade and a k−5/3 power law is used to study critical points of these fields.
The velocity stagnation point based pair separation model of Goto and Vassilicos
(S Goto and J C Vassilicos, 2004, New J.Phys., 6, p.65) is revisited and placed on a
sound mathematical foundation. The DNS is used to study the time-asymmetry observed
between forward and backward separation. A new method has been employed to obtain
values for the Richardson constants and the ratio of them for the backwards and forwards
case, which is gb/gf = (0.92±0.03) and hence, exhibits a qualitatively different behaviour
from pair separation in three-dimensional turbulence, where gb > gf (J Berg et al. , 2006,
Phys.Rev.E, 74(1), p.016304). An explanation for this behaviour based on the timeasymmetry
related to the inverse versus forward energy cascade is suggested.
Zero Acceleration Points (ZAPs) and flow structures around them are studied using
the same DNS. A well-defined classification of ZAPs in terms of the acceleration gradient
tensor’s (∇a) invariants is presented. About half of all ZAPs are Anti-ZAPs (with
det[∇a] < 0) and the number of vortical and straining ZAPs (with det[∇a] > 0) is about
the same. Vortical and straining ZAPs are swept by the local fluid velocity to a good
statistical approximation whereas Anti-ZAPs are not. The average life-time of ZAPs
seems to scale with the time-scale of the smallest eddies in the turbulence, though ZAPs
(in particular vortical ones) are able to survive up to a few integral time scales. The new
ZAP classification can also be applied to extended flow regions and a discussion of the
length-scales and sizes characterising these regions and the distances between ZAPs is
given.
velocity and acceleration field of two-dimensional turbulence. A direct numerical simulation
(DNS) of two-dimensional homogeneous isotropic turbulence with an inverse energy
cascade and a k−5/3 power law is used to study critical points of these fields.
The velocity stagnation point based pair separation model of Goto and Vassilicos
(S Goto and J C Vassilicos, 2004, New J.Phys., 6, p.65) is revisited and placed on a
sound mathematical foundation. The DNS is used to study the time-asymmetry observed
between forward and backward separation. A new method has been employed to obtain
values for the Richardson constants and the ratio of them for the backwards and forwards
case, which is gb/gf = (0.92±0.03) and hence, exhibits a qualitatively different behaviour
from pair separation in three-dimensional turbulence, where gb > gf (J Berg et al. , 2006,
Phys.Rev.E, 74(1), p.016304). An explanation for this behaviour based on the timeasymmetry
related to the inverse versus forward energy cascade is suggested.
Zero Acceleration Points (ZAPs) and flow structures around them are studied using
the same DNS. A well-defined classification of ZAPs in terms of the acceleration gradient
tensor’s (∇a) invariants is presented. About half of all ZAPs are Anti-ZAPs (with
det[∇a] < 0) and the number of vortical and straining ZAPs (with det[∇a] > 0) is about
the same. Vortical and straining ZAPs are swept by the local fluid velocity to a good
statistical approximation whereas Anti-ZAPs are not. The average life-time of ZAPs
seems to scale with the time-scale of the smallest eddies in the turbulence, though ZAPs
(in particular vortical ones) are able to survive up to a few integral time scales. The new
ZAP classification can also be applied to extended flow regions and a discussion of the
length-scales and sizes characterising these regions and the distances between ZAPs is
given.
Date Issued
2010
Date Awarded
2010-02
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Vassilicos, John Christos
Creator
Faber, Tristan Friedrich
Publisher Department
Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)