Schematic of organized coherent flow motion known as a superstructure and its interaction across the turbulent boundary layer. Credit: Science, Marusic et al. Click to enlarge. |

Researchers at the University of Melbourne (Australia) are proposing a mathematical model for predicting fluid flows close to surfaces (near-wall turbulence) given only large-scale information from the outer boundary layer region. This predictive capability may enable new strategies for the control of turbulence and may provide a basis for improved engineering to reduce drag in ships and aircraft and in weather prediction simulations.

Research team leader and Federation Fellow Professor Ivan Marusic from the Department of Mechanical Engineering at the University of Melbourne says skin-friction drag accounts for 50% of fuel expenditure in aircraft, so even modest reductions in drag would save money and significantly reduce carbon emissions. This proportion of drag-induced fuel expenditure is higher still for a large oil tanker or submarine.

When air flows over a surface, skin friction drag is created. Most of this drag is a result of the chaotic and unpredictable nature of the boundary layer—the layer immediately between the object and the airflow. Accurate knowledge of how this air flows over a surface will provide engineers with more detailed information about resistance.—Ivan Marusic

In addition to energy expenditure, turbulent boundary layers also promote increased mixing, heat transfer, and exchange processes; thus, when they occur on an atmospheric scale, they have important meteorological and climatological implications, the team writes in a paper on their findings in the 9 July issue of the journal *Science*.

Computer simulations of wall-bounded turbulence are extremely challenging because the simulation must resolve the entire range of scales of turbulent motion. For a boundary layer that has developed over the length of a large aircraft fuselage, these motions could range from the meter scale down to just a few micrometers for the smallest dissipative motions. Atmospheric surface layers will have similar scale separation, with the largest scales on the order of 1 km and the smallest around 1 mm.

In general, turbulent boundary layers are characterized by the dimensionless parameter known as the Reynolds number (Re), which is essentially the ratio of the largest inertial scale to the smallest dissipative scale in the flow. To date, even the largest supercomputers can solve such flows only at comparatively low Re values, which are several orders of magnitude below most practical applications. In overcoming this limitation, one approach has been large-eddy simulation, in which a sparse grid is used to resolve the large-scale motions, whereas the unresolved small-scale motions are modeled. For high-Re wall-bounded flows, this also requires a near-wall model to account for the relationship between the wall shear stress and the outer-layer flow.

This current work aims to improve our understanding of this complex interaction, offering a simple mathematical model that can accurately predict near-wall turbulent statistics based only on large-scale outer-layer information.—Marusicet al.

In a Perspective in the same issue of Science, Dr. Ronald Adrian from Arizona State University also notes that:

Turbulence created when fluids flow past surfaces, called wall turbulence, affects the flux of water vapor and CO_{2}from the ocean’s surface, causes drag on airplanes and ships, and influences how atmospheric pollutants are transported near Earth’s surface. Wall turbulence presents a particularly difficult computational problem, because very small motions that occur in a thin inner layer near the wall must be modeled accurately. This inner layer is critical because it contains the region where the effects of molecular transport mechanisms, such as viscosity, resist the transport of momentum, heat, and/or mass between the wall and the fluid. These motions cannot be described in sufficient detail with direct computation; the number of grid points within the layer where numerical calculations would need to be performed would lead to an impractically large task.

...Marusic et al. show that fluctuating turbulent motions within the inner layer respond to the larger-scale outer motions in two ways, thus connecting their average behaviors. The large outer motions add to the small-scale inner motions, and they also modulate the amplitude of the inner motions. The additive effect is not entirely unexpected, but the amplitude modulation effect is a nonlinear coupling that had not been anticipated. Using this model, Marusic et al. could remove the nonuniversal contributions of the outer flow from the inner flow, leaving a more universal inner layer that is amenable to empirical representation.

These findings relate to one of the grand challenges in the science and engineering of fluid dynamics: the development of governing equations that can be solved by numerical methods so as to reliably predict turbulent flow.

**Resources**

I. Marusic, R. Mathis, N. Hutchins (2010) Predictive Model for Wall-Bounded Turbulent Flow.

*Science*. Vol. 329. no. 5988, pp. 193 - 196 doi: 10.1126/science.1188765Ronald J. Adrian (2010) Closing In on Models of Wall Turbulence.

*Science*. Vol. 329. no. 5988, pp. 155 - 156 doi: 10.1126/science.1192013