On stratified steady periodic water waves with linear density distribution and stagnation points

We use bifurcation theory to construct small periodic gravity stratified water waves with density which depends linearly upon the pseudostream function. As a special feature the density may also decrease with depth and the waves we obtain may posses two different critical layers with catʼs eye vortices. Within the vortex, the density of the fluid has an extremum at the stagnation point.