Imperial College London


Faculty of EngineeringDepartment of Aeronautics

Professor of Computational Fluid Mechanics



+44 (0)20 7594 5052s.sherwin Website




313BCity and Guilds BuildingSouth Kensington Campus






BibTex format

author = {Mao, X and Blackburn, HM and Sherwin, SJ},
doi = {10.1017/jfm.2015.304},
journal = {Journal of Fluid Mechanics},
pages = {241--265},
title = {Nonlinear optimal suppression of vortex shedding from a circular cylinder},
url = {},
volume = {775},
year = {2015}

RIS format (EndNote, RefMan)

AB - This study is focused on two- and three-dimensional incompressible flow pasta circular cylinder for Reynolds number Re 6 1000. To gain insight into themechanisms underlying the suppression of unsteadiness for this flow we determinethe nonlinear optimal open-loop control driven by surface-normal wall transpiration.The spanwise-constant wall transpiration is allowed to oscillate in time, althoughsteady forcing is determined to be most effective. At low levels of control cost,defined as the square integration of the control, the sensitivity of unsteadiness withrespect to wall transpiration is a good approximation of the optimal control. Thedistribution of this sensitivity suggests that the optimal control at small magnitude isachieved by applying suction upstream of the upper and lower separation points andblowing at the trailing edge. At high levels of wall transpiration, the assumptionsunderlying the linearized sensitivity calculation become invalid since the base flowis eventually altered by the size of the control forcing. The large-magnitude optimalcontrol is observed to spread downstream of the separation point and draw the shearlayer separation towards the rear of the cylinder through suction, while blowingalong the centreline eliminates the recirculation bubble in the wake. We furtherdemonstrate that it is possible to completely suppress vortex shedding in two- andthree-dimensional flow past a circular cylinder up to Re = 1000, accompanied by70 % drag reduction when a nonlinear optimal control of moderate magnitude (withroot-mean-square value 8 % of the free-stream velocity) is applied. This is confirmedthrough linearized stability analysis about the steady-state solution when the nonlinearoptimal wall transpiration is applied. While continuously distributed wall transpirationis not physically realizable, the study highlights localized regions where discretecontrol strategies could be further developed. It also highlights the appropriate rangeof application of
AU - Mao,X
AU - Blackburn,HM
AU - Sherwin,SJ
DO - 10.1017/jfm.2015.304
EP - 265
PY - 2015///
SN - 1469-7645
SP - 241
TI - Nonlinear optimal suppression of vortex shedding from a circular cylinder
T2 - Journal of Fluid Mechanics
UR -
UR -
VL - 775
ER -