The energy spectrum of fronts: time evolution of shocks in Burgers' equation

Abstract

Andrews and Hoskins used semigeostrophic theory to argue that the energy spectrum of a front should decay like the -8/3 power of the wavenumber. They note, however, that their inviscid analysis is restricted to the very moment of breaking; that is, to the instant t=tB when the vorticity first becomes infinite. In this paper, Burgers' equation is used to investigate the postbreaking behavior of fronts. We find that for t>tB, the front rapidly evolves to a jump discontinuity. Combining our analysis with the Eady wave/Burgers' study of Blumen, we find that the energy spectrum is more accurately approximated by the -8/3 power of the wavenumber, rather than by the k-2 energy spectrum of a discontinuity, for less than two hours after the time of breaking. -from Author