Embedding formulae for wave diffraction by a circular arc

For certain wave diffraction problems, embedding formulae can be derived, which represent the solution (or far-field behaviour of the solution) for all plane wave incident angles in terms of solutions of a (typically small) set of other auxiliary problems. Thus a complete characterisation of the scattering properties of an obstacle can be determined by only determining the solutions of the auxiliary problems, and then implementing the embedding formula. The class of scatterers for which embedding formulae can be derived has previously been limited to obstacles with piecewise linear boundaries; here this class is extended to include a simple curved obstacle, consisting of a thin circular arc. Approximate numerical calculations demonstrate the accuracy of the new embedding formulae. •Embedding formulae of use as they reduce effort required for full characterisation of diffraction properties of scatterer.•Formulae here for first time derived for simple curved scatterer.•Derivation using direct approach from boundary-value problem, and also via formulation as integral equation.•Numerical calculations demonstrate implementation and use of embedding formulae.