A finite-difference method for solving the time-dependent Navier- Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an ap- plication to a three-dimensional convection problem is presented.

/pdf/numerical-solution-of-the-navier-stokes-equations-1d4r986mvf.pdf

Numerical solution of the Navier-Stokes equations

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.

/pdf/on-the-nature-of-turbulence-51oqh4n2pn.pdf

On the nature of turbulence

https://jxshix.people.wm.edu/2013-taiwan/crandall-rabinowitz-1971-JFA.pdf

Bifurcation from simple eigenvalues

A finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an application to a three-dimensional convection problem is presented.

Numerical Solution of the Navier-Stokes Equations*

/pdf/on-the-nature-of-turbulence-x9h2lslftq.pdf

P. H. Rabinowitz

Papers

Existence and nonuniqueness of rectangular solutions of the Bénard problem