## Overview

This is a summary. There is a website dedicated to my research.

My research is in the field of theoretical fluid dynamics, with strong emphasis on mathematics, and a wide scope, ranging from classical theoretical problems such as the high-Reynolds-number asymptotics of the steady solution of the Navier-Stokes equations for the flow past a bluff body to applied works such as the proposal of a practical method of turbulent drag reduction.

Currently active research areas are:

- Application of the polynomial Sum-Of-Squares (SOS) approach in fluid dynamics. See also the Sum-Of-Squares project website.

- Turbulence, in particular organised structures and drag reduction, with a special interest in application of linearsied Navier-Stokes equations to these problems, and in the high-Reynolds-number effects.

I continue to be very interested in the recent research areas:

- Easy-to-use Navier-Stokes solvers (Flow Illustrator and Interactive Flow Illustrator)

- Flow control, in particular control of separated flows in vortex cells.

PhD projects would preferably be offered in one of the currently active areas. However, for those students who are *really* interested in any of the areas of my past activity an exception can be made. Collaborations are invited in any of the areas mentioned here.

## Main research achievements

- Most well-known result (first published in Russian in 1988) is the high-Reynolds-number asymptotics of the steady solution of the Navier-Stokes equations for the flow past a bluff body. The Reynolds number Re is the only parameter entering the steady Navier-Stokes equations. Two great fluid dynamicists, George G. Stokes and Ludwig Prandtl, found the asymptotics for small Re (Stokes, in 1851) and the asymptotics for high Re for streamlined bodies (Prandtl, in 1904). The solution of the last remaining problem of high-Re asymptotics for a bluff body closed more than a century-long chapter in the history of classical fluid dynamics.
- In a short paper published in 1984 it was demonstrated that in typical cases when the number density of dust particles in a gas tends to infinity on the envelope of their trajectories, the mean distance between particles remains finite. This justified the use of the known formula for the drag force of an isolated particle even on the envelope of particle trajectories. Since such situations are the rule rather than the exception this result paved the way for modelling dusty-gas flows, and it was widely exploited by other researchers.
- The paper published in the Journal of Fluid Mechanics in 2005 contibutes to a new conceptual framework in the theory of streak formation in near-wall turbulence, provides convincing arguments in its favour, and develops a mathematical tool demonstrating its significant predictive ability. For more than half a century since their discovery streaks were generally believed to be created by some other coherent structures present in the flow, and numerous suggestions were made about the nature of these structures. In that paper it was demonstrated that the physical mechanisms involved have their own structure-forming properties, which determine some of streak characteristics independently of whether or not streaks are formed by other organised structures.
- A method for applying Sum of Squares of polynomials technique to fluid dynamics proposed in a paper published in Physica-D in 2012 promises many advances in various areas. This work is in progress, see the SoS website.
- The latest result I consider of wide significance is described in an arxiv paper demonstrating that the recently discovered effect of modulation of near-wall turbulence by the outer large-scale structures is largely quasi-steady.

**Other research covered a rather wide area of fluid dynamics, including:**

Nonlinear stability of air-cushion vehicles, turbulent supersonic separated flows with heat and mass injection in the separation region, three-dimensional separation, hydraulically driven centrifuges, trapped vortices, rotating stall in axial compressors, flow control, existence of the solutions of he Navier-Stokes equations, and various questions of computational fluid dynamics and high-Reynolds-number asymptotics of fluid flows. Vast majority of these studies were purely mathematical, but a few were applied, and some of the studies had more engineering nature; in particular, research on centrifuges was conducted in close association with a team of engineers, and resulted in author's certificates (Soviet equivalent of patents) rather than papers.

## Funding

- Principal Investigator, EPSRC, EP/J011126/1, 2013-2016, £336,962 (for Imperial College team). "Sum-of-Squares Approach to Global Stability and Control of Fluid Flows"
- Co-investigator (PI Prof. M Leschziner), EPSRC, EP/G061556/1, 2009-2012, £342,188 (for Imperial College team). "Investigation of alternative drag-reduction strategies in turbulent boundary layers by using wall forcing"
- Principal Investigator, Airbus/EPSRC, EP/F004672, 2007-2008, £191,978, ÂFluidic control for turbulent drag reduction''
- Scientific Coordinator, EC Framework 6, contract number AST4-CT-2005-012139, 2005-2008, €1,800,000, "Fundamentals of actively controlled flows with trapped vortices"
- Scientific Coordinator, EU Framework 6, FP6-2006-TTC-TU-Priority-4, 2006-2008, €132000, "ÂFundamentals of Actively Controlled Flows with Trapped Vortices, Extension"
- Principal Investigator, EPSRC, GR/S67029, 2004-2007, £69,071 (£138,171 with services included) "Master-mode analysis of the genesis of organised structures in turbulent flows"
- Principal Investigator, EPSRC, EP/D050871/1, 2006-2009, £140,540, "Numerical study of turbulent flow in eccentric annular pipes"
- Co-Investigator, EPSRC, GR/S82947/01 PLATFORM, "Turbulence Platform", 2004-2009, 2004-2009, £395,873. Jointly with Prof. J.C. Vassilicos (Principal Investigator, Imperial College), Prof. I.P. Castro, Dr. G.N. Coleman (both Southampton), Prof. M.A. Leschziner, Prof. J. Morrison (both Imperial College), Prof. N.D. Sandham (Southampton)
- Royal Society (International incoming short visit) grant, 2006, £3,832, on "Generalised optimal perturbation approach to predicting turbulent streaks"
- Principal Investigator, EPSRC, GR/R27785/01, 2001-2004, £59,894, on "Mechanism of longitudinal vortices in near-wall turbulent flow"
- Royal Society (Europian Science Exchange), 2002-2003, Ref no 13872, £8,175, jointly with Prof. Luca Zannetti (Politecnico di Torino, Italy), on "Active control of trapped vortices";
- Principal Investigator, International Science Foundation, Grant M4K000, $11,775, 1994, on "High-Reynolds-number Batchelor-model flows"
- Principal Investigator, International Science Foundation, Grant M4K30, $6,482, 1995, on "High-Reynolds-number Batchelor-model flows"
- Principal Investigator, Russian Foundation for Basic Research, Project 96-01-01290, 1996-1998 (amount in roubles made meaningless by inflation but it was substantial for Russian researchers at the time of receipt), on "Mathematical theory of rotating stall"
- Principal Investigator, Russian Foundation for Basic Research, Project 93-01-17622,1993-1995, (Co-PI Prof. A.A.Barmin), on "Construction of mathematical models and investigation of heat and mass transfer processes with phase transitions and chemical reactions in natural porous mediums and volcanic systems"

Before 1993 no funding was made on competitive basis in Russia.