Electron. J. Differential Equations, Vol. 2020 (2020), No. 104, pp. 1-21.

Short term unpredictability of high Reynolds number turbulence - rough dependence on initial data

Zaichun Feng, Y. Charles Li

Abstract:
Short term unpredictability is discovered numerically for high Reynolds number fluid flows under periodic boundary conditions. Furthermore, the abundance of the short term unpredictability is also discovered. These discoveries support our theory that fully developed turbulence is constantly driven by such short term unpredictability.

Submitted January 5, 2020. Published October 12, 2020.
Math Subject Classifications: 76F02, 76F06, 76F20, 76F05, 76F30.
Key Words: Short term unpredictability; rough dependence on initial data; turbulence; chaos; sensitive dependence on initial data.
DOI: 10.58997/ejde.2020.104

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Zaichun Feng
Department of Mechanical and Aerospace Engineering
University of Missouri
Columbia, MO 65211, USA
email: fengf@missouri.edu
Y. Charles Li
Department of Mathematics
University of Missouri
Columbia, MO 65211, USA
email: liyan@missouri.edu, http://faculty.missouri.edu~liyan

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