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1. The problem of turbulence
 
2. Auxiliary functions
 
3. Sum of squares
 
4. Orbits in space
 
5. Accelerating averaging
 
Download the video (116Mb)           Download the archived version. (85Mb)
A talk on this topic is available from the of Workshop IV: Turbulence in Engineering Applications, Long Program Mathematics of Turbulence, IPAM 2014..
Download the video (90Mb)           Download the archived version. (108Mb)
Download the video (90Mb)           Download the archived version. (85Mb)
An abbreviated videorecord (68 Mb) of an overview talk on applications of linearized Navier-Stokes equations to developed turbulence and turbulent drag reduction (Mathematics of Turbulence programme, IPAM, 2014)
         Download the archived version.
These leaflets are now outdated. They show how my views and interests evolved.
Application of the polynomial Sum-Of-Squares (SOS) approach in fluid dynamics.
Organised structures and drag reduction in turbulent flows.
Control of separated flows in vortex cells.
Try it, it is easy and !
Bounding time averages: a road to solving the problem of turbulenceat Institut de Mathématiques de Bordeaux, Bordeaux, May 4, 2023.
Auxiliary functionals: a path to solving the problem of turbulenceat on March 4, 2021. Links to and .
Accelerating time averagingat 73rd Annual Meeting of the APS Division of Fluid Dynamics, November 22, 2020: and video.
Accelerating time averaging using auxiliary functionsat the Aerodynamics and Flight Mechanics group seminar, University of Southampton, on 6 February 2019
Large-scale motions for the QSQH theory(with Chi Zhang).
Questions concerning quasi-steady mechanism of the Reynolds number, pressure gradient, and geometry effect on drag reductionat the Aachen, Germany, 15-16 March 2018.
Sergei Chernyshenko