Turbulence-driven corrugation of fast-mode shock waves

Collisionless shocks are often modelled as smooth, planar surfaces - but many show organized corrugations that steer how particles get accelerated and how they radiate. We present a simple, linear magnetohydrodynamic (MHD) model that treats the shock as an evolving interface. This lets us separate two things: (1) the shock’s own properties and geometry, and (2) the statistics of the upstream turbulence that hits it. With this separation, we obtain a
direct map from incoming fluctuations to the corrugation patterns they create, including their drift speed and coherence. In our model, the interface acts like an “impedance” that focuses broad-band turbulent power into fast-mode waves that skim along the shock. The shock responds most strongly when the wave’s normal group speed is small (a sharp, single-peaked response). Corrugation strength increases with compression, while the shock geometry and plasma beta control how long these patterns persist. The framework makes testable predictions linking upstream turbulence and shock shape to fine
structure in electromagnetic signals from heliospheric and supernova-remnant shocks.