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PreprintCC BY 4.0arXiv

Unification of The Navier-Stokes Equation for Fluid Mechanics and Aeroacoustics

  • Tapan K. Sengupta
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Abstract

The Navier-Stokes equation for a compressible Newtonian fluid is reassessed, in view of recent investigation results on the foundations of aeroacoustics. In the process, the role and necessity of the so-called Stokes' hypothesis is reconsidered, which in its current practice omits the bulk viscosity. In contrast, the relevance of a new generalized kinematic viscosity is proposed, along with a new methodology that will enable estimation of second coefficient of viscosity completely obviating the necessity of making the Stokes' hypothesis. This opens up the vista of a new formulation for the Navier-Stokes equation applicable for both the subjects of fluid mechanics and aeroacoustics in a unified approach.

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Cite

BibTeXRIS
BibTeX
@misc{sengupta2026unification,
  title = {{Unification of The Navier-Stokes Equation for Fluid Mechanics and Aeroacoustics}},
  author = {Tapan K. Sengupta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06457},
  eprint = {2609.06457},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06457},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Unification of The Navier-Stokes Equation for Fluid Mechanics and Aeroacoustics
AU  - Tapan K. Sengupta
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06457
UR  - https://arxiv.org/abs/2609.06457
AB  - The Navier-Stokes equation for a compressible Newtonian fluid is reassessed, in view of recent investigation results on the foundations of aeroacoustics. In the process, the role and necessity of the so-called Stokes' hypothesis is reconsidered, which in its current practice omits the bulk viscosity. In contrast, the relevance of a new generalized kinematic viscosity is proposed, along with a new methodology that will enable estimation of second coefficient of viscosity completely obviating the necessity of making the Stokes' hypothesis. This opens up the vista of a new formulation for the Navier-Stokes equation applicable for both the subjects of fluid mechanics and aeroacoustics in a unified approach.
ER  -