  In this paper, we investigate the two-dimensional extension of a recently
introduced set of shallow water models based on a regularized moment expansion
of the incompressible Navier-Stokes equations
\cite{kowalski2017moment,koellermeier2020analysis}. We show the rotational
invariance of the proposed moment models with two different approaches. The
first proof involves the split of the coefficient matrix into the conservative
and non-conservative parts and prove the rotational invariance for each part,
while the second one relies on the special block structure of the coefficient
matrices. With the aid of rotational invariance, the analysis of the
hyperbolicity for the moment model in 2D is reduced to the real
diagonalizability of the coefficient matrix in 1D. Then we prove the real
diagonalizability by deriving the analytical form of the characteristic
polynomial. Furthermore, we extend the model to include a more general class of
closure relations than the original model and establish that this set of
general closure relations retain both rotational invariance and hyperbolicity.
