$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\halfi}{{1/2}}
\newcommand{\xpoint}{\boldsymbol{x}}
\newcommand{\normalvec}{\boldsymbol{n}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\Ix}{\mathcal{I}_x}
\newcommand{\Iy}{\mathcal{I}_y}
\newcommand{\It}{\mathcal{I}_t}
\newcommand{\setb}[1]{#1^0} % set begin
\newcommand{\sete}[1]{#1^{-1}} % set end
\newcommand{\setl}[1]{#1^-}
\newcommand{\setr}[1]{#1^+}
\newcommand{\seti}[1]{#1^i}
\newcommand{\Real}{\mathbb{R}}
$$
Numerical dispersion relation in 2D (2)
$$ \frac{\tilde c}{c} = \frac{1}{Ckh}
\sin^{-1}\left(C\left(\sin^2 ({\half}kh\cos\theta)
+ \sin^2({\half}kh\sin\theta) \right)^\half\right)
$$
Can make color contour plots of \( 1-\tilde c/c \) in
polar coordinates with \( \theta \) as the angular coordinate and
\( kh \) as the radial coordinate.
