Recognizing the importance of stable modes improves models of shear-driven turbulence

When one fluid slips along another, this sheared flow can excite unstable modes that grow in amplitude and form turbulence. Shear-driven turbulence is readily simulated at low flow speeds, but computers aren’t powerful enough to directly simulate it at high flow speeds, such as those encountered in astrophysical systems. However, “reduced” models could help predict what happens at high flow speeds without direct simulation. In reduced models, turbulence is expressed as a combination of different modes, or patterns of motion in the fluid, at different spatial scales. Reduced models of shear-driven turbulence help explain how ionized matter, called plasma, diffuses around newly formed stars, as well as describe turbulence in Earth’s magnetotail and other processes.

The state of a collective dynamical system, like a flowing plasma, can be described by its contributing modes, each characterized by a spatial structure and an oscillating frequency. When approximating large spatial scales in reduced models of the shear-driven turbulence, standard practice has been to consider only unstable modes, which initially grow in amplitude until turbulence develops and the modes couple nonlinearly.

But in a new analysis, Adrian Fraser and his co-authors carefully examined if stable modes, which do not initially grow, matter in the turbulent state. They simulated an unstable shear flow that drives turbulence, and compared the contribution of different modes. The authors found that stable modes, which initially decay in amplitude over time, do indeed matter almost as much as unstable modes. When they added stable modes to the reduced models, the models performed better and correctly predicted the flow shear and intensity of the resulting turbulence. Without the stable modes, the models sometimes falsely predicted that the turbulence would decrease when driven harder.

Their work is the first to demonstrate that stable modes are important in large scale turbulence. Fraser said that their findings indicate that they’re starting to find the right tools to understand systems of shear-driven turbulence. Next, the authors plan to study a plasma system, known as the free shear layer, which is more relevant to astrophysical systems.

Source: “Role of stable modes in driven shear-flow turbulence,” by A. E. Fraser, M. J. Pueschel, P. W. Terry, and E. G. Zweibel, Physics of Plasmas (2018). The article can be accessed at https://doi.org/10.1063/1.5049580 .