Spacecraft observations of interplanetary shocks have
revealed significant deviations in energetic particle spectra from
the diffusive shock acceleration (DSA) theory predictions. Within
almost two decades of particle energy, spanning about seven e-folds
upstream, the particle flux is almost energy independent. Although
at and behind the shock, it falls off as $\epsilon^{-1}$ (as predicted
by DSA for reasonably strong shocks), the flux decreases with the
coordinate close to the shock upstream progressively steeper at lower
energies, which leads to a flat energy distribution. Within a standard
DSA solution under a fixed turbulence spectrum, pre-existing or self-excited
by accelerated particles, a flat particle spectrum over an extended upstream area
means that the particle diffusivity must be energy-independent,
contrary to most transport models. We propose a resolution of this
paradox by invoking a strongly nonlinear solution upstream under a
self-driven but short-scale turbulence, in which the particle diffusivity
increases with energy as $\propto\epsilon^{3/2}$, but also decays
with the wave energy as $1/E_{\text{w}}$, which compensate for the $\epsilon^{3/2}$
rise. The main difference with the traditional DSA is that the wave-particle
interaction is nonresonant, and the turbulence is not saturated at
the Bohm level (that would require $\delta B\sim B_{0}$ turbulence
saturation amplitude). A steep, energy-dependent final drop in the
particle flux far ahead of the shock to its background level in the solar wind
is likely due to a quick particle escape upstream caused
by turbulence deficiency.