Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors

Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors

An analytical solution to the Navier–Stokes momentum equations for a compressible flow with volume and small shear viscosities as well as external friction is presented while the dynamic viscosity is set to zero. The demonstrated methodology holds in d dimensions. However, in this study, the three-d...

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Main Author: Yahya Öz
Format: Article
Language:English
Published: AIP Publishing LLC 2021-05-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/5.0050330
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spelling doaj-337aac11b55e4fb38fa93f2d05783f902021-06-01T18:31:02ZengAIP Publishing LLCAIP Advances2158-32262021-05-01115055009055009-610.1063/5.0050330Rigorous investigation of the Navier–Stokes momentum equations and correlation tensorsYahya Öz0Advanced Materials, Processes and Energies Technology Center, Turkish Aerospace, 06980 Ankara, TurkeyAn analytical solution to the Navier–Stokes momentum equations for a compressible flow with volume and small shear viscosities as well as external friction is presented while the dynamic viscosity is set to zero. The demonstrated methodology holds in d dimensions. However, in this study, the three-dimensional case is considered in detail. The analytical solution blows up at finite times T, which is determined by a cubic relation if the initial flow velocity is not divergence-free. The existence of T is a necessary and sufficient condition for implementing a singularity. Nonetheless, for external friction μe>T−1, all analytical expressions are smooth while the averaged expressions are smooth for all times.http://dx.doi.org/10.1063/5.0050330
collection DOAJ
language English
format Article
sources DOAJ
author Yahya Öz
spellingShingle Yahya Öz
Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
AIP Advances
author_facet Yahya Öz
author_sort Yahya Öz
title Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
title_short Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
title_full Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
title_fullStr Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
title_full_unstemmed Rigorous investigation of the Navier–Stokes momentum equations and correlation tensors
title_sort rigorous investigation of the navier–stokes momentum equations and correlation tensors
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2021-05-01
description An analytical solution to the Navier–Stokes momentum equations for a compressible flow with volume and small shear viscosities as well as external friction is presented while the dynamic viscosity is set to zero. The demonstrated methodology holds in d dimensions. However, in this study, the three-dimensional case is considered in detail. The analytical solution blows up at finite times T, which is determined by a cubic relation if the initial flow velocity is not divergence-free. The existence of T is a necessary and sufficient condition for implementing a singularity. Nonetheless, for external friction μe>T−1, all analytical expressions are smooth while the averaged expressions are smooth for all times.
url http://dx.doi.org/10.1063/5.0050330
work_keys_str_mv AT yahyaoz rigorousinvestigationofthenavierstokesmomentumequationsandcorrelationtensors
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