# The Turbulence of Dimples

Turbulence shows up everywhere we look: from the flight of airplanes to golf balls, or the fluttering of a flag to the swinging of suspension bridges. Through the eyes of a fluid dynamicist, “smooth sailing” is something of a rare exception. Turbulence is a type of flow characterized by chaotic and rapid changes in the properties of flow. Yet even though it is commonplace, the physics and mathematics of turbulence are extraordinarily complex, and still very active areas of research. In spite of these difficulties, engineers are constantly confronted by the challenge of dealing with turbulence in their designs because of its ubiquity and importance. Proper understanding and attention could help prevent another Tacoma Narrows Bridge.

Physicists and engineers often use dimensionless numbers to help talk about and characterize complex phenomena. When it comes to turbulence, at the heart of every discussion is the Reynolds number, named after the British fluid dynamicist Osborne Reynolds. The Reynolds number measures the relative importance of inertial forces to viscous forces in any flow, so an increased Reynolds number corresponds to dominating inertial forces, which results in more chaotic behavior.

Another important factor is the patterns or texture of the surface over which the flow takes place. Shark skin, with its small riblet structures aligned with the motion direction, interacts with the turbulent flow of water slipping past in ways that reduce drag on the animal, enabling it to be a fast swimmer. Dimpled surfaces also interact with turbulent flows in interesting ways. The surfaces of golf balls work to decrease drag and increase the flight distance.

Usually, any feature that results in increased turbulence, improves mixing at the expense of a significant increase in fluidic drag. A ceiling fan stirs up the air in a room. If you want more air mixing you need to crank up the speed, but this will make the motor work harder. How hard the motor is working is a measure of the fluidic drag. Thus, increased drag is usually undesirable because it requires more power to drive the motion.

Under certain conditions however, dimples on the walls of a conduit can be arranged in such a way that they dramatically improve mixing with only little increase in drag. Such designs find applications in heat exchangers, where improved mixing results in higher heat exchanger efficiencies without paying a proportionally large penalty on the pumping costs.

Above, we show results of high performance computational fluid dynamics simulations of turbulent air flow over dimpled surfaces. Even though the flow would be turbulent in the absence of dimples, presence of dimples gives rise to the formation of additional structures in the flow. For example, rolling vortices shedding off the dimpled cavities are evident in the 1st clip (moderate Reynolds number), which help improve mixing. The second clip examines the variation of flow velocity in just a vertical slice of the total flow, that also occurs at a lower speed. The last video shows a very similar flow but at a faster flow speed (high Reynolds number).