Gallery Of Vector Fields

$(x,0)$ §

\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.16}

\begin{document}
\begin{tikzpicture}
\begin{axis}[axis equal, view = {0}{90}, axis lines = center]
    % Normal vectors
    \addplot3[
        cyan,
        quiver={
            u={x},  % x-component of normal
            v={0},  % y-component of normal
            w={0},             % z-component of normal
            scale arrows=0.7,
        },
	    domain=-4:4,
        -stealth,
        samples=10,
		mark=*,
	    mark options={scale=0.4, fill=black}, % dots at arrow tails
    ]
    {0};
\end{axis}
\end{tikzpicture}
\end{document}

$(0,-y)$ §

\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.16}

\begin{document}
\begin{tikzpicture}
\begin{axis}[axis equal, view = {0}{90}, axis lines = center]
    % Normal vectors
    \addplot3[
        cyan,
        quiver={
            u={0},  % x-component of normal
            v={-y},  % y-component of normal
            w={0},             % z-component of normal
            scale arrows=0.5
        },
	    domain=-4:4,
        -stealth,
		mark=*,
	    mark options={scale=0.4, fill=black}, % dots at arrow tails
        samples=10,
    ]
    {0};
\end{axis}
\end{tikzpicture}
\end{document}

$(x,-y)$ §

\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.16}

\begin{document}
\begin{tikzpicture}
\begin{axis}[axis equal, view = {0}{90}, axis lines = center]
    % Normal vectors
    \addplot3[
        cyan,
        quiver={
            u={x},  % x-component of normal
            v={-y},  % y-component of normal
            w={0},             % z-component of normal
            scale arrows=0.5
        },
	    domain=-4:4,
        -stealth,
		mark=*,
	    mark options={scale=0.4, fill=black}, % dots at arrow tails
        samples=10,
    ]
    {0};
\end{axis}
\end{tikzpicture}
\end{document}

$(-y,x)$ §

\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.16}

\begin{document}
\begin{tikzpicture}
\begin{axis}[axis equal, view = {0}{90}, axis lines = center]
    % Normal vectors
    \addplot3[
        cyan,
        quiver={
            u={-y},  % x-component of normal
            v={x},  % y-component of normal
            w={0},             % z-component of normal
            scale arrows=0.5
        },
	    domain=-4:4,
        -stealth,
		mark=*,
	    mark options={scale=0.4, fill=black}, % dots at arrow tails
        samples=10,
    ]
    {0};
\end{axis}
\end{tikzpicture}
\end{document}

$(y,-x,2)$ §

\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.16}

\begin{document}
\begin{tikzpicture}
\begin{axis}[axis lines = center]
    \addplot3[
	    mesh,
	    black,
	    variable = t,
	    domain = 0:2*pi,
	    samples = 20
    ] ({sin(deg(t)}, {cos(deg(t))}, {2*t});
    % Normal vectors
    \addplot3[
        cyan,
        quiver={
            u={y},  % x-component of normal
            v={-x},  % y-component of normal
            w={2},             % z-component of normal
            scale arrows=0.3
        },
        -stealth,
		mark=*,
	    domain = 0:2 *pi,
	    y domain = 0:4*pi,
	    mark options={scale=0.4, fill=black}, % dots at arrow tails
        samples=10,
    ] ({sin(deg(x)}, {cos(deg(x))}, {y});
	\addplot3[
	red,
	quiver={
		u={y},  % x-component of normal
		v={-x},  % y-component of normal
		w={2},             % z-component of normal
		scale arrows=0.3
	},
	-stealth,
	mark=*,
	domain = 0:2 *pi,
	mark options={scale=0.4, fill=black}, % dots at arrow tails
	samples=10,
] ({sin(deg(x)}, {cos(deg(x))}, {2*x});

\end{axis}
\end{tikzpicture}
\end{document}