  In this paper we apply the approach of formal asymptotic expansions and
perturbation theory to derive a new highly nonlinear shallow-water model from
the full governing equations for two dimensional incompressible fluid with
constant vorticity. This approximate model is generated by introduction of a
larger scaling than the Camassa-Holm one, which is shown to be optimal in the
sense that there are no non-local terms appearing in free surface equation.
Moreover, we establish the local well-posedness of the Cauchy problem in Besov
spaces, and give a blow-up criterion, which improve the previous corresponding
results in Sobolev spaces.
