We study the evolution of an accelerating hyperrelativistic shock under the presence of upstream inhomogeneities wrinkling the discontinuity surface. The investigation is conducted by means of numerical simulations using the PLUTO code for astrophysical fluid dynamics. The reliability and robustness of the code are demonstrated against well-known results coming from the linear perturbation theory. We then follow the nonlinear evolution of two classes of perturbing upstream atmospheres and conclude that no lasting wrinkle can be preserved indefinitely by the flow. Finally, we derive analytically a description of the geometrical effects of a turbulent upstream ambient on the discontinuity surface.
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