Visualizing Small Navier Stokes Equation (∇•ū = 0)

[James Brady]

TL;DR Summary

i’m trying to picture the divergence in an intentional cube and i’m getting wacky answers.

the thickness of the line segment represent a faster fluid. wouldn’t all of these be positive divergence just in different directions?

 

[boneh3ad]

FYI, $\nabla\cdot\vec{u}=0$ is not a "small Navier-Stokes equation." It's the continuity equation for an incompressible fluid. It states that the divergence of the velocity field (i.e., the dilatation of the fluid element passing through that flow field) is zero.

I am not really sure what you are trying to do otherwise. Where's the confusion here? Is it just the sign convention? You have to pick some direction to be positive, and in your example, you've defined all velocities as positive, so in some cases you will be showing positive or negative dilatation based on that.