Abstract
The ‘numerically exact’ properties of plane periodic deep-water waves are used in a slowly-varying-wave approximation for a steady axisymmetric wave field. The linear ‘ray’ theory for such a wave field corresponds to waves approaching a circular caustic. A parameter, C, characterizes each solution. If C is smaller than 20 the wave behaviour is dominated by the convergence of wave energy and waves are expected to break. Comparison with experiment for C = 0 indicates that breaking may be accurately predicted. If C is greater than 50 then the waves propagate closer to the caustic and, since it is of Peregrine & Smith's (1979) type R, it is likely that the waves do not break. These solutions show that wave action does not flow along the straight lines of the linear rays.
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