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The study aims to explore steady solutions to the Euler equations for two-dimensional flow with constant vorticity layers.

Large‐Amplitude Periodic Solutions to the Steady Euler Equations With Piecewise Constant Vorticity

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The study aims to explore steady solutions to the Euler equations for two-dimensional flow with constant vorticity layers.
Analyzed steady solutions using global bifurcation theory.
Constructed solution curves terminating with stagnation points or breakdown of conformal equivalence.
Utilized a novel elliptic system formulation for velocity components in each layer.
Applied conformal mappings and horizontal distortion to ensure agreement at the interface.
Provided numerical evidence of flow behavior depending on parameters.
Either a corner forms on the interface or one layer develops very thin regions.
Introduced the first local formulation addressing multi-layer problems in fluid dynamics.

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This research reveals periodic solutions of fluid flow in a channel with variable vorticity, suggesting models for complex flows.

Doak et al. (2026) studied this question.

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