Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session X37: Non-Newtonian Flows: Turbulence & Instabilities
8:00 AM–10:23 AM,
Tuesday, November 21, 2023
Room: 203AB
Chair: Prabir Daripa, Texas A&M University
Abstract: X37.00002 : Lundgrens Infinite Hierarchy of Probability Density Functions for Linear Viscoelastic Materials*
8:13 AM–8:26 AM
Presenter:
Johannes H Conrad
(TU Darmstadt)
Authors:
Johannes H Conrad
(TU Darmstadt)
Simon Görtz
(Tu Darmstadt)
Martin Oberlack
(TU Darmstadt)
The governing equations have recently been extended to the treatment of compressible flows, and the treatment of active- and magnetohydrodynamic turbulence. However, no such description of viscoelastic turbulence yet exists.
To obtain a formally closed description of viscoelastic turbulence, the introduction of multi-time probability density functions is proposed, capturing the temporally non-local nature of the Cauchy stress tensor. These density functions convey the probability of observing the velocities v1 through vN at N separate spatiotemporal points, within some infinitesimal phase-space volumes dvi. Finally, a Lungren-type hierarchy is obtained by utilizing the deterministic one-point momentum equations. Although the current framework only allows for the treatment of linear viscoelastic materials, its extension to the more general Walter’s fluids is discussed.
*Johannes Conrad and Simon Görtz are supported by the Graduate School CE at TU Darmstadt.
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