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Stream/Area:
-
Subject:
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Paper ID:
10.55041/IJSREM.ISTCESD023
Volume:
10 |
9 |
Sep 2026
Pages:
1-3
Publication Frequency:
Monthly (12 issues per year)
License:International Journal of Scientific Research in Engineering and Management follows the Creative Commons Attribution 4.0 (CC BY 4.0) License, allowing free use and distribution with proper attribution.
Department of Mathematics
Late Nitin College, Pathri Dist Parbhani.
The inviscid limit describes the behavior of a viscous fluid as its kinematic viscosity approaches zero. Although this limit can be difficult to analyze in the presence of solid boundaries because of the formation of thin boundary layers, the problem becomes considerably cleaner on a periodic two-dimensional domain. In this paper, the incompressible Navier–Stokes equations on the two-dimensional torus T² are considered to examine the transition from viscous flow to the corresponding ideal Euler flow. The vorticity formulation is used to study the effects of viscosity on vorticity transport, kinetic energy, and dissipation. A Taylor–Green vortex provides a simple numerical framework for illustrating the influence of decreasing viscosity on the persistence of coherent flow structures. The analysis indicates that, in the periodic two-dimensional setting, viscous solutions approach the inviscid dynamics as viscosity tends to zero, while the direct contribution of viscous dissipation becomes increasingly small. The periodic geometry therefore provides a useful baseline for studying the inviscid limit without the additional complications introduced by solid-wall boundary layers.
KEYWORDS
The 2D incompressible Navier–Stokes equations on a periodic domain provide a clear framework for studying the inviscid limit. As ν → 0⁺, viscous diffusion weakens, dissipative energy loss vanishes, and dynamics approach Euler equations without boundary-layer interference.
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Publication Date
9/28/2026
Peer Review Type
Double-Blind Peer Review
Review Rounds: 2
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