Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3327
Abstract
An analytical solution to the incompressible Navier-Stokes momentum equations for a divergence-free flow $\boldsymbol{\nabla}\cdot \vec u\left(\vec x,t\right)=0$ with time-dependent dynamic viscosity $\mu\left(t\right)$ is presented. The demonstrated methodology holds for the physically relevent three dimensions. The constructed flow velocities $\vec u\left(\vec x,t\right)$ are eigenvectors of the vector operator curl. Moreover, vortex $\vec \omega\left(\vec x,t\right)$, helicity $H\left(\vec x,t\right)$, enstrophy $\mathcal{E}\left(t\right)$ and enstrophy evolution $\frac{\mathrm{d}\mathcal{E}\left(t\right)}{\mathrm{d}t}$ are explicitly determined.
Keywords
Flow behavior, fluid dynamics, partial differential equations
First Page
3192
Last Page
3200
Recommended Citation
ÖZ, YAHYA
(2022)
"Novel exact solutions to Navier-Stokes momentum equations describing an incompressible fluid,"
Turkish Journal of Mathematics: Vol. 46:
No.
8, Article 9.
https://doi.org/10.55730/1300-0098.3327
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss8/9
