What is it about?

Turbulent flow is often described as chaotic and unpredictable, but at the same time many phenomena governed by turbulent flow are robust and predictable, such as the drag of a car or the lift of an airplane. Due to the complexity of turbulence its mathematical description is often statistical in nature, whereas a detailed representation of the turbulent flow structures demands powerful supercomputers. In this article we show that, in fact, turbulent flow can be decomposed into a sum of three fundamental components that are simple to describe mathematically, each with its own specific stability property. A stability analysis based on this triple decomposition provides a new tool to describe and to predict turbulent flow.

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Why is it important?

The stability analysis is based on the fundamental Navier-Stokes equations and gives new insights into perturbation growth in turbulence, the dynamics of vorticity, and the computability of turbulent flow. These new insights can be used, for example, to describe the structure of turbulent flow on different scales, and possibly to shine new light on mathematical questions like the Onsager conjecture and the regularity of the Navier-Stokes equations.


Stability analysis of turbulent flow has been restricted to simple model problems, or worst case estimates of general turbulent flow which have provided little insight. In this article we use the triple decomposition of the turbulent flow in a detailed stability analysis that distinguishes between the different flow structures, thereby also suggesting a scenario for how the turbulent flow structures evolve over time.

Johan Hoffman
Kungliga Tekniska Hogskolan

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This page is a summary of: Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor, Physics of Fluids, August 2021, American Institute of Physics, DOI: 10.1063/5.0060584.
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