Theoretical analysis derives exact pressure-gradient identities for material deformation in incompressible Euler flow, showing spherical means depend strictly on local strain tensor magnitude.
This paper studies a specific question in incompressible Euler flow: what happens to material particle motion when the local deformation is not exactly affine? I do not present this as a solution to the Euler regularity problem, and I do not claim to build a new turbulence model. The contribution is narrower: I write down a deterministic identity for a link that is often left to modelling or approximation in cluster-based and multi-particle descriptions. This law shows that the spherical mean depends only on the size of the local strain tensor.
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Fares Alabdali (2026) studied this question.
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