Steady solutions to the Navier-Stokes equations

O. M. Podvigina


The paper presents results of computing steady solutions to the three-dimensional Navier--Stokes equations with periodic boundary conditions and with the force proportional to the ABC flow. For the force inversely proportional to the Reynolds number $R$, the ABC flow is a steady solution for any $R$. In the considered case $A$=$B$=$C$=1 we found six other families of steady solutions. Three mutually symmetric families emerge at $R\approx7.9$; the other three, also mutually symmetric, emerge at $R\approx149$. The families were traced numerically up to \hbox{$R$=1000--2000}; presumably they persist at any arbitrary larger~$R$.

Back to
Computational Seismology, Vol. 5.