  Oceanic waves registered by satellite observations often have curvilinear
fronts and propagate over various currents. In this paper, we study long linear
and weakly-nonlinear ring waves in a stratified fluid in the presence of a
depth-dependent horizontal shear flow. It is shown that despite the clashing
geometries of the waves and the shear flow, there exists a linear modal
decomposition (different from the known decomposition in Cartesian geometry),
which can be used to describe distortion of the wavefronts of surface and
internal waves, and systematically derive a 2+1 - dimensional cylindrical
Korteweg-de Vries - type equation for the amplitudes of the waves. The general
theory is applied to the case of the waves in a two-layer fluid with a
piecewise-constant current, with an emphasis on the effect of the shear flow on
the geometry of the wavefronts. The distortion of the wavefronts is described
by the singular solution (envelope of the general solution) of the nonlinear
first-order differential equation, constituting generalisation of the
dispersion relation in this curvilinear geometry. There exists a striking
difference in the shape of the wavefronts of surface and interfacial waves
propagating over the same shear flow.
