Self-similar solutions to the Navier-Stokes equations
In Ohkitani-Vanon (2022) an expression for the linearised
forward self-similar profile is explicitly obtained to
the incompressible Navier-Stokes equations. The next aim is
to determine the nonlinear self-similar profile numerically
and characterise it theoretically.
Effects of advection on the regularity of flow fields
We modify the Navier-Stokes equations in velocity gradient form
by weakening their advection with a parameter. The current aim is to investigate
how the properties of solutions change with the change of the parameter.
Comparison of Navier-Stokes flows in the whole space and the periodic domain
In Ohkitani (2023) we compared direct numerical simulations of 2D Navier-Stokes
equations on the while plane and the periodic domain. The present aim is to do a similar
comparison in three dimensions.
Interpolation between the Navier-Stokes and Burgers equations.
We consider a system which is equivalent to the Burgers equations
by rotating the velocity gradient in 2D incompressible Navier-Stokes equations.
Introducing a generalised system by interpolation between them,
we study numerically how the solutions change in properties with the change of
the rotation angle. Furthermore we introduce a similar interpolation in three dimensions
to see what is happening therein.