Turbulence and Coherent Structures, Control and Computation

From COSNet

Vale Edward Lorenz, 1917- 16 April 2008, one of the pioneers of chaos theory.

(News item added by Rowena Ball 22/04/08.)

--Ball7 12:07, 22 April 2008 (EST)

A comprehensive understanding of fluid turbulence and how to control it remains one of the grandest, yet most formidable, challenges in science and engineering. In a turbulent flow all possible scales of motion, from the smallest scales, where viscosity dominates the advection and dissipates the energy of fluid motion, to the effective size of the system, typically coexist and interact in subtle and surprising ways. For instance, in flows that are effectively three-dimensional (3D) the folding and stretching of small parcels of fluid allows efficient mixing and downscale net energy transport, while flows that are effectively two-dimensional (2D) exhibit poor mixing and upscale net energy cascade. The multi-scale, nonlinear nature of turbulence makes it a complex systems problem.

Turbulence is ubiquitous in the real world with fundamental problems occurring across disciplines such as combustion and other reactive flows, engineering fluid dynamics, space and astrophysics, plasma physics and in environmental fluid dynamics. Turbulence plays a significant role in mixing and heat and mass transfer applications and research in this area is driven by a need to predict and accurately model the onset of turbulence. Because of its breadth of application the study of turbulent fluid flows is a truly multi-disciplinary venture with advances in one area informing developments in other areas.

There is not one "problem of turbulence" but several

• transition to turbulence - one mechanism or many?
• 3D turbulence in

• a) shear flows unbounded (boundary layers, jets, wakes, mixing layers)
• b) shear flows confined (Taylor-Couette flow, pipes, ducts)
• c) body force fields (buoyancy driven)

• 2D turbulence (large-scale geophysical and astrophysical flows, low-frequency turbulence in magnetised plasmas)
• dispersive (weak) turbulence (surface water waves, high-frequency plasma waves)
• emergence of quasi-coherent large-scale structures (zonal flows planetary atmospheres and magnetically confined plasmas, atmospheric blocking)
• self-organisation and phase transitions describable by a finite number of order parameters (emergence of low-dimensional behaviour)
• emergence of finite-time singularities - wave breaking, collapse
• avalanching behaviour - self-organised criticality (fusion and astrophysical plasmas)
• mixing (passive advection)

Many applications require the active control and management of turbulence. In the aerodynamics and acoustics industries, for example, the objectives are drag reduction and noise control and the focus of research is on the design and implementation of strategies to inhibit the onset of turbulence. The potential economic benefits that will arise from new drag reduction technologies are enormous.

Active control strategies for these applications require a deep understanding of the transition from laminar to turbulent flow and how this process is affected by external conditions. Implementing control strategies requires real time simulation of the transition process. Recent advances have been made via the links between fluid dynamicists (experimental, computational and theoretical), control theory specialists and computational scientists. This theme will further these developments by facilitating the interaction between researchers in fluid turbulence across a wide discipline base.

In turbulence research we are only just beginning to tap the potential for exploitation of the self-organising properties of quasi two-dimensional flows. In applications based on the fundamental statistical mechanics of upscale energy transfer in such flows we are interested in various facets of flow control after the onset of turbulence. The vanguard has been led by fusion plasma confinement research, where progress towards the goal of economical self-sustained fusion is driven by the imperative of controlling turbulent mass and energy transport. Here the general strategy is to harness the self-organising properties of the flow to achieve control over transport barrier induction and relaxation.

In non-plasma flows there is enormous potential for exploiting upscale energy transfer into coherent structures as a means of primary fluid component sequestration. Many industrial flows contain advected particles of different densities, such as process streams from textile or forest industries, bio-pharmaceutical micro-fluid processing, waste waters, or effluents from chemical reactors. There is an identified need for more economical and environmentally friendly methods of primary treatment of such fluids, ie., differential sequestration of fluid constituents for enrichment or depletion.

The global climate is governed by a large number of interacting sub-systems (atmosphere, oceans, clouds, vegetation, etc). In the atmosphere localized shear and zonal flows are important controllers of turbulent eddies and barriers to heat and particle mixing. These are natural processes that we need to understand more fully in the context of weather and climate prediction in Australia, pollutant and volcanic ash dispersal, ozone dynamics, the enhanced greenhouse effect, and other anthropogenic environmental perturbations. In the oceans the biology and population dynamics of very small marine organisms such as schools of krill is very tightly coupled to their turbulent physical environment, to an extent that is not felt by large land animals in air.

Turbulent flow control is important inside living organisms too. The bio-functionality of many protein motors, such as the cilia that enable us to hear, is tightly coupled to their fluid-turbulent physical environment and the consequent collective dynamics of multiple units. In these complex systems, turbulence length and time scales are of the order of the time constants for molecular turnover and key reaction rate constants.

In space, one finds complexity and self-organisation deriving from plasma-physical effects, coupling of multiple elements of systems, and gravitational many-body interactions. For instance, the brightness and variability of the aurora, as well as the dynamics of energetic particles and magnetic fields in Earth's magnetosphere and ionosphere (e.g., spacecraft radiation events and magnetic substorms), are well-described as self-organized complex systems. Other turbulent space weather phenomena like solar flares and associated X-ray events obey similar relationships.