Hey dear users

**Background:** Imagine we have the time-dependent incompressible Navier-Stokes equations with an initial condition and no-slip (homogeneous Dirichlet boundary) on the whole boundary, i.e.

$$\begin{aligned} \partial_t u - \nu \Delta u+(u \cdot \nabla)u+\nabla p = f \\ \text{div} u=0 \\ u(x,0)=u_0(x) \text{ on } \Omega \\ u=0 \text{ on } (0,T)\times \partial\Omega\end{aligned}$$

As the space domain Iād like to take a bounded Lipschitz domain (e.g. C^1 boundary), so I just took a ball as my first test. And this ball is filled with some fluid - e.g. water. Further I want to take an initial condition that is quadratically integrable, i.e. u(x,0)=u_0(x) on \Omega and u_0 \in L^2(\Omega). And a outer force f \in L^2((0,T) \times \Omega) in the Navier-Stokes equations.

**What I want to do:** I wanted to have some āniceā and āinterestingā results that happen inside the ball. Some rotation or some sorts. This is not that easy for me to achive with only using no-slip boundary and no inlets/outlets Of course, taking an uniform initial condition just leads to a uniform result.

Do you have some ideas what I could do to get a nice result?

I thought of taking an initial condition that gets me some rotation. But I could only take uniform initial conditions with SimScale and I had some problems with the āRotating Zonesā and āSolid Body Motionā options in this specific case. Could you maybe tell me what I should do in these options?

The project is the following: https://www.simscale.com/workbench?publiclink=9235df82-c3d8-4583-b8e8-a1d5e0fb9ea3

I just imported a ball and generated a mesh, nothing much.

Thank you so much,

Marvin