Weak-strong uniqueness and extreme wall events at high Reynolds number

Weak Euler solutions have been hypothesized to explain the d'Alembert paradox of non-vanishing drag. A difficulty is the ``weak-strong uniqueness'' property, which requires that an admissible weak Euler solution must coincide with the smooth Euler solution for the same initial data. Using the Josephson-Anderson relation adapted from superfluids, we show that weak-strong uniqueness for d'Alembert's solution requires mild conditions. To explain drag we therefore predict that these conditions are violated by violent eruption of very thin boundary layers. We discuss observational signatures and explain how the small length-scales involved could threaten the validity of a hydrodynamic description.

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Publication Details

Journal
Physical Review Fluids
Published
2025-06-09
DOI
https://doi.org/10.1103/physrevfluids.10.064610
Citations
2
Primary Topic
Fluid Dynamics and Turbulent Flows
Type
article
Field-Weighted Citation Impact
2.67

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article

Weak-strong uniqueness and extreme wall events at high Reynolds number

Gregory L. Eyink, Hao Quan
2 citations
Physical Review Fluids
Fluid Dynamics and Turbulent Flows
2.67
article

Weak-strong uniqueness and extreme wall events at high Reynolds number

Gregory L. Eyink, Hao Quan
article en
2 citations

Abstract

Weak Euler solutions have been hypothesized to explain the d'Alembert paradox of non-vanishing drag. A difficulty is the ``weak-strong uniqueness'' property, which requires that an admissible weak Euler solution must coincide with the smooth Euler solution for the same initial data. Using the Josephson-Anderson relation adapted from superfluids, we show that weak-strong uniqueness for d'Alembert's solution requires mild conditions. To explain drag we therefore predict that these conditions are violated by violent eruption of very thin boundary layers. We discuss observational signatures and explain how the small length-scales involved could threaten the validity of a hydrodynamic description.

Physical Review FluidsVol. 10(6)
Johns Hopkins University (US)
Simons Foundation, European Research Council, Horizon 2020
Climate action
Openalex Percentile: Top 12%
Fluid Dynamics and Turbulent Flows
2.67
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