Relationship between the methods of bounding time averages

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Title: Relationship between the methods of bounding time averages
Authors: Chernyshenko, S
Item Type: Working Paper
Publication Date: 2017-04-08
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.
Issue Date: 8-Apr-2017
Copyright Statement: © 2017 The Author(s)
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/J011126/1
Keywords: physics.flu-dyn
Notes: 10 pages. This second version corrects a typo in (12), without any other changes
Appears in Collections:Faculty of Engineering

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