How can I draw a vector field without using a function?

Question

I want to write an essay about vector fields, and give an example using the bath-tub example. I want to get a figure similar to this one:

The figure source: https://www.youtube.com/watch?v=0jW74lrpeM0&t=269s

Also if there's any function that produces a similar figure it's okay.

Answer 1

Is that what you want? I just decorate with arrows along the Bezier curves.

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[myarr/.style={decoration={markings,
mark=between positions 0.08 and .96 step #1
with { 
\draw[-stealth] (-.15,0)--(.15,0);
}},postaction={decorate}}]

%\draw[gray!50] (-2,-2) grid (6,2);
\clip (-2,-2) rectangle (6,2);
\path[red,myarr=.2] (0,0)--(4,0);
\path[red,myarr=.15] (0,0) .. controls +(30:1) and +(180-30:1) .. (4,0);
\path[red,myarr=.15] (0,0) .. controls +(60:1.5) and +(180-60:1.5) .. (4,0);
\path[red,myarr=.1] (0,0) .. controls +(90:2) and +(180-90:2) .. (4,0);
\path[red,myarr=.08] (0,0) .. controls +(120:3) and +(180-120:3) .. (4,0);
\path[red,myarr=.04] (0,0) .. controls +(150:6) and +(180-150:6) .. (4,0);
\path[red,myarr=.02] (0,0) .. controls +(165:15) and +(180-165:15) .. (4,0);
\path[red,myarr=.12] (0,0)--(-2,0) (6,0)--(4,0);

\path[red,myarr=.15] (0,0) .. controls +(-30:1) and +(180+30:1) .. (4,0);
\path[red,myarr=.15] (0,0) .. controls +(-60:1.5) and +(180+60:1.5) .. (4,0);
\path[red,myarr=.1] (0,0) .. controls +(-90:2) and +(180+90:2) .. (4,0);
\path[red,myarr=.08] (0,0) .. controls +(-120:3) and +(180+120:3) .. (4,0);
\path[red,myarr=.04] (0,0) .. controls +(-150:6) and +(180+150:6) .. (4,0);
\path[red,myarr=.02] (0,0) .. controls +(-165:15) and +(180+165:15) .. (4,0);

\fill[blue] (0,0) circle(2pt) (4,0) circle(2pt);
\end{tikzpicture}
\end{document}