Drawing circle with inner splines

Question

any suggestion on how to draw the splines within the circle shown in this figure:

with TikZ?

Answer 1

Sadly, due to the rounded corners, there are a few inaccuracies that make the arrow tips not align correctly to the paths. It would have been possible to directly decorate the paths, but then again the exact positioning on the path is difficult to calculate.

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings, arrows.meta}

\begin{document}

\begin{tikzpicture}[>=Stealth]

    \draw (0,0) circle (2);
    
    \foreach \r/\s in {1.6/.2, 1.2/.6} {
        \draw[rounded corners] 
            ({acos(\s/\r)}:\r) arc 
            ({acos(\s/\r)}:{-acos(\s/\r)}:\r) -- 
            cycle;
        \draw[rounded corners] 
            ({180+acos(\s/\r)}:\r) arc 
            ({180+acos(\s/\r)}:{180-acos(\s/\r)}:\r) -- 
            cycle;
    }
    
    \foreach \a/\r/\t in {
        75/2/255, 105/2/105, 75/-2/255, 105/-2/105,
        0/.2/0, 30/1.6/210, -30/1.6/150, 
        0/.6/0, 30/1.2/210, -30/1.2/150, 
        0/-.2/0, 30/-1.6/210, -30/-1.6/150, 
        0/-.6/0, 30/-1.2/210, -30/-1.2/150
    } {
        \draw[draw=none, postaction={decorate}, 
            decoration={markings, mark=at position .5 with {\arrow[rotate=\t]{>}}}] 
            ([yshift=-1pt]\a:\r) -- ([yshift=1pt]\a:\r);
    }
    
    \draw[->] (0,1.6) -- (0,2);
    \draw[->] (0,-2) -- (0,-1.6);

    \draw[-{>[open]}] (0,2.6) node[right] {$w_\infty$} -- (0,2.2);
    
\end{tikzpicture}

\end{document}