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arXiv · 2609.16442

A Differential Algebraic Framework for Boundary Layer $α$-Models

C. Valencia-Negrete·J. Flores·M. Perez·M. Romero de Terreros·M. Favela
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Abstract

By addressing the problem of describing the differences between the saturation monoids of the Prandtl and Leray-$α$ boundary layers, and algebraically distinguishing the action of the Helmholtz operator, we can show that, when the modification of the vector field is halted at a minimum scale determined by the differential filter, the paradox of constructing a solution that reaches infinite velocity in a finite time is avoided. Furthermore, it allows us to obtain the coefficients of the Taylor expansion near the wall for boundary layers where the Helmholtz operator has been applied.

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C. Valencia-Negrete, J. Flores, M. Perez, M. Romero de Terreros, M. Favela. 2026-09-14. A Differential Algebraic Framework for Boundary Layer $α$-Models. https://arxiv.org/abs/2609.16442

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