When a fluid flows along a boundary, irregularities in the surface of the boundary cause frictional drag, which in turn creates “tumbling” in the fluid, or turbulence. Turbulence is everywhere in everyday life—its effects govern the flow of rivers and oil pipelines, the drag on airplanes and baseballs, and even the circulation of blood in our bodies.
Despite its importance, however, turbulence is not well understood. Even today, engineers cannot accurately predict the pressure needed to force a fluid such as oil or natural gas through a pipeline at a desired rate; instead they infer flow rates from phenomenological charts based on experiments that were done in the 1930s.
The long-sought connection between frictional drag and the eddies in fluid flow, first proposed by Gustavo Gioia
, Pinaki Chakraborty and Nigel Goldenfeld
at the University of Illinois
, has been tested experimentally, as reported today in Nature Physics
. The measurements were performed by a team from the University of Illinois at Urbana-Champaign (Tuan Tran, Pinaki Chakraborty, Nicholas Guttenberg, in addition to Gioia and Goldenfeld), from the University of Pittsburgh (Alisia Prescott and Walter Goldburg
), and from the University of Bordeaux (Hamid Kellay
In these experiments, a vertically flowing soap film held between two wires is pierced by a turbulence-inducing comb, and the fluid motion is probed by laser beams. The soap film is thin enough that the fluid behaves as if it were two-dimensional, not three-dimensional. The setup measures both the two-dimensional turbulent velocity fluctuations and the frictional drag at the bounding wires.
The theory predicts that in two-dimensional fluids, because of the relationship between the fluctuations and the drag, the drag should have a special dependence on the flow speed, different from that observed in regular three-dimensional turbulent pipe flow. The new experiments fully support the Illinois theoretical work, but are outside the realm of standard textbook expectations, dating back to the early 20th century.
Although turbulence remains a deeply challenging problem, progress has occurred because the investigators asked a new question: How can we connect the small-scale fluctuations in the turbulent fluid to the large-scale effects of turbulent drag? According to the team that conducted the experiment, the implications of the work have practical applications: for example, it can be used to predict how to transport oil and gas through long pipelines at lower energy cost, by adding polymer molecules to the fluid to make it flow with less drag.