What Does It Take to Tame Turbulence?

Professor Mohamed Gad-el-Hak
Department of Aerospace & Mechanical Engineering
University of Notre Dame
Notre Dame, IN 46556, USA
E-Mail: gadelhak@goliath.fz-rossendorf.de

Despite over a century of intensive research, turbulence remains largely an enigma, analytically unapproachable yet practically very important. For a turbulent flow, the dependent variables are random functions of space and time, and no straightforward method exists for analytically obtaining stochastic solutions to the governing nonlinear, partial differential equations. The statistical approach to solving the Navier-Stokes equations always leads to more unknowns than equations (the closure problem), and solutions based on first principles are again not possible. Turbulence, therefore, is a conundrum that appears to yield its secrets only to physical and numerical experiments, provided that the wide band of relevant scales is fully resolved a far-from-trivial task at high Reynolds numbers.

Consistent with the unattainability of rational, analytical solutions to turbulent flow problems and with the difficulties of physical and numerical experiments at high Reynolds numbers, controlling a practical turbulent flow to achieve a desired effect such as drag reduction, lift enhancement or noise abatement is also a very difficult task. Passive control methods, while always preferable, are limited in their utility by the problem practical constraints. Brute force suppression, or taming, of turbulence via active, energy-consuming control devices is always possible, but the penalty for doing so often exceeds any potential savings. The challenge is to achieve a desired effect with minimum energy expenditure. The present talk will emphasize the energy cost/benefit involved with a variety of reactive control strategies targeted at specific coherent structures and with the sole objective of suppressing turbulence. Such methods may include the use of suction/injection, wall heating/cooling, surface motion or, most relevant to this meeting, the use of Lorentz force field.


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