Universal power law for the energy spectrum of breaking Riemann waves

The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation. The spectrum of spatial amplitudes at the breaking time t = tb has an asymptotic decay of k−4/3, with corresponding energy spectrum decaying as k−8/3. This spectrum is formed by the singularity of the form (x − xb)1/3 in the wave shape at the breaking time. This result remains valid for arbitrary nonlinear wave speed. In …