  Testing the order of accuracy of (very) high order methods for shallow water
(and Euler) equations is a delicate operation and the test cases are the
crucial starting point of this operation. We provide a short derivation of
vortex-like analytical solutions in 2 dimensions for the shallow water
equations (and, hence, Euler equations) that can be used to test the order of
accuracy of numerical methods. These solutions have different smoothness in
their derivatives (up to $\mathcal C^\infty$) and can be used accordingly to
the order of accuracy of the scheme to test.
