October 19, 2025Open Access

Unraveling Self-Similar Energy Transfer Dynamics: a Case Study for 1D Burgers System

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Authors

PMPritpal MatharuMax Planck Institute for Mathematics in the Sciences BPBartosz ProtasMcMaster University TYTsuyoshi YonedaHitotsubashi University

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Implication

This analysis reveals energy transfer dynamics through self-similar solutions in one-dimensional viscous flows, suggesting implications for turbulence models.

Key Points

Self-similar solutions exhibit unique energy transfer behavior, with distinct viscous and inertial cases influencing enstrophy.
The study identifies two solution families where enstrophy decays or grows, directly linked to viscosity and Fourier space interactions.
Utilizing PDE-constrained optimization, local solutions were derived using an adjoint-based gradient method for more accurate flow modeling.
The findings provide a foundational proof of concept for exploring self-similar dynamics in complex three-dimensional turbulence.

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Matharu et al. (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc696fed https://doi.org/10.48550/arxiv.2507.12764

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Implication

This analysis reveals energy transfer dynamics through self-similar solutions in one-dimensional viscous flows, suggesting implications for turbulence models.

Unraveling Self-Similar Energy Transfer Dynamics: a Case Study for 1D Burgers System

Discussion

Member takes

Implication

Key Points

Cite This Study

Unraveling Self-Similar Energy Transfer Dynamics: a Case Study for 1D Burgers System

Discussion

Member takes

Implication

Key Points

Cite This Study

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