  We present surprising observations by the NASA Van Allen Probes spacecraft of
whistler waves with substantial electric field power at harmonics of the
whistler wave fundamental frequency. The wave power at harmonics is due to
nonlinearly steepened whistler electrostatic field that becomes possible in the
two-temperature electron plasma due to whistler wave coupling to the
electron-acoustic mode. The simulation and analytical estimates show that the
steepening takes a few tens of milliseconds. The hydrodynamic energy cascade to
higher frequencies facilitates efficient energy transfer from cyclotron
resonant electrons, driving the whistler waves, to lower energy electrons.
