Relationship between the methods of bounding time averages
File(s)
Published version
Author(s)
Chernyshenko, S
Type
Working Paper
Abstract
The problem of finding bounds of time-averaged characteristics of dynamical
systems, such as for example the bound on the mean energy dissipation rate in a
turbulent flow governed by incompressible Navier-Stokes equations, is
considered. It is shown that both the well-known background flow method of
Doering and Constantin and the direct method proposed by Seis in 2015
correspond to the same quadratic storage functional in the framework of the
indefinite storage functional method. In particular, a background flow can be
found corresponding to the linear functional used in the direct method and vice
versa. It is shown that any bound obtained with the background flow method can
also be obtained by the direct method. The reverse is true subject to an
additional constraint. The relative advantages of the three methods are
discussed.
systems, such as for example the bound on the mean energy dissipation rate in a
turbulent flow governed by incompressible Navier-Stokes equations, is
considered. It is shown that both the well-known background flow method of
Doering and Constantin and the direct method proposed by Seis in 2015
correspond to the same quadratic storage functional in the framework of the
indefinite storage functional method. In particular, a background flow can be
found corresponding to the linear functional used in the direct method and vice
versa. It is shown that any bound obtained with the background flow method can
also be obtained by the direct method. The reverse is true subject to an
additional constraint. The relative advantages of the three methods are
discussed.
Date Issued
2017-04-08
Citation
2017
Copyright Statement
© 2017 The Author(s)
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://arxiv.org/abs/1704.02475v2
Grant Number
EP/J011126/1
Subjects
physics.flu-dyn
physics.flu-dyn
Notes
10 pages. This second version corrects a typo in (12), without any other changes