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Polynomial sum of squares in fluid dynamics: a review with a look ahead

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Title: Polynomial sum of squares in fluid dynamics: a review with a look ahead
Authors: Chernyshenko, SI
Goulart, P
Huang, D
Papachristodoulou, A
Item Type: Journal Article
Abstract: The first part of this paper reviews the application of the sum-of-squares-of-polynomials technique to the problem of global stability of fluid flows. It describes the known approaches and the latest results, in particular, obtaining for a version of the rotating Couette flow a better stability range than the range given by the classic energy stability method. The second part of this paper describes new results and ideas, including a new method of obtaining bounds for time-averaged flow parameters illustrated with a model problem and a method of obtaining approximate bounds that are insensitive to unstable steady states and periodic orbits. It is proposed to use the bound on the energy dissipation rate as the cost functional in the design of flow control aimed at reducing turbulent drag.
Issue Date: 28-Jul-2014
Date of Acceptance: 1-Jul-2014
URI: http://hdl.handle.net/10044/1/15496
DOI: 10.1098/rsta.2013.0350
ISSN: 1364-503X
Publisher: The Royal Society
Start Page: 1
End Page: 18
Journal / Book Title: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume: 372
Issue: 2020
Copyright Statement: © 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/J011126/1
Keywords: Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
sum of squares of polynomials
flow stability
bounds for turbulent dissipation
flow control
TURBULENT SHEAR FLOWS
LOW-DIMENSIONAL MODEL
OPTIMIZATION PROBLEMS
STABILITY ANALYSIS
RELAXATIONS
PROGRAMS
SPARSITY
DESIGN
BOUNDS
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
sum of squares of polynomials
flow stability
bounds for turbulent dissipation
flow control
TURBULENT SHEAR FLOWS
LOW-DIMENSIONAL MODEL
OPTIMIZATION PROBLEMS
STABILITY ANALYSIS
RELAXATIONS
PROGRAMS
SPARSITY
DESIGN
BOUNDS
bounds for turbulent dissipation
flow control
flow stability
sum of squares of polynomials
General Science & Technology
Publication Status: Published
Article Number: 20130350
Online Publication Date: 2014-07-28
Appears in Collections:Aeronautics
Faculty of Engineering



This item is licensed under a Creative Commons License Creative Commons