Potential–Vortical Decomposition and Spatial Mode Closure for the Incompressible Navier–Stokes Equations

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The incompressible Navier-Stokes equations can be reformulated into an ensemble of ordinary differential equations through potential-vortical decomposition and spatial mode closure of the non-linear and viscous terms. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Martínez Suazo Herman Jahzeel

doi:10.5281/zenodo.22259049

September 2, 2026Open Access

Potential–Vortical Decomposition and Spatial Mode Closure for the Incompressible Navier–Stokes Equations

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Key Points

Formulate a potential–vortical decomposition and spatial mode closure for the incompressible Navier–Stokes equations to resolve nonlinear and viscous interactions.
Separated fluid velocity fields into potential and vortical components within the incompressible Navier–Stokes framework.
Derived a spatial mode closure strategy to transform continuous partial differential equations into a discrete ensemble of ordinary differential equations.
Demonstrated exact mathematical treatment and decoupling of nonlinear advection and viscous diffusion terms across spatial modes.
Successfully converted continuous fluid dynamical field equations into a computationally tractable ensemble of coupled ordinary differential equations.

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Implication

Theoretical analysis demonstrates spatial mode closure in incompressible fluid dynamics, suggesting a practical reduction of Navier–Stokes equations to an ensemble of ordinary differential equations.

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Martínez Suazo Herman Jahzeel (2026) studied this question.

synapsesocial.com/papers/6a9a862b5d9e33f25c631c36 https://doi.org/10.5281/zenodo.22259049

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Potential–Vortical Decomposition and Spatial Mode Closure for the Incompressible Navier–Stokes Equations

Key Points

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Implication

Abstract

Discussion

Cite This Study

Potential–Vortical Decomposition and Spatial Mode Closure for the Incompressible Navier–Stokes Equations

Key Points

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Implication

Abstract

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