Check also the links to videos on the timeline =>.
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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 record of an earlier talk on this topic is available from the website 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These leaflets are now outdated.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 it is fun!
Oberwolfach Workshop 2431 - Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms, and Applicationsat the Mathematisches Forschungsinstitut Oberwolfach, Germany 28 July - 2 August 2024.
Studying fluid flows with auxiliary functions and LMIsat the IFAC World Congress, held in Yokohama, Japan on 8-14th July 2023.
Bounding time averages: a road to solving the problem of turbulenceat Institut de Mathématiques de Bordeaux, Bordeaux, May 4, 2023.
Bounding time averagesand
How quasi-steady is the modulation of near-wall turbulence by large-scale structures?(with Yunjiu Yang).
Auxiliary functionals: a path to solving the problem of turbulenceat The Seminar in the Analysis and Methods of PDE (SIAM PDE) on March 4, 2021. Links to the abstract and the video.
Accelerating time averagingat 73rd Annual Meeting of the APS Division of Fluid Dynamics, November 22, 2020: abstract and video.
Accelerating time averaging using auxiliary functionsat the Aerodynamics and Flight Mechanics group seminar, University of Southampton, on 6 February 2019
Coherent structures in wall-bounded turbulence: new directions in a classic problem, London, August 29-31, 2018, with a talk
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 Workshop on Active Drag Reduction, Aachen, Germany, 15-16 March 2018.
The problem of turbulence: bounding solutions to equations of fluid mechanics & other dynamical systems, with Giovanni Fantuzzi providing exercise sessions, at The 6th Bremen Winter School
Dynamical systems and turbulence, March 12-16, 2018.
Sergei Chernyshenko