Inviscid scaling in the Kuramoto-Sivashinsky equation from functional renormalization group and direct numerical simulations (opens in new tab)

We show that the one-dimensional Kuramoto-Sivashinsky (KS) equation features a scaling regime characterized by the dynamical exponent $z=1$ at intermediate scales between the large-scale Kardar-Parisi-Zhang (KPZ) scaling with $z=3/2$ and the small-scale non-universal behavior. This scaling regime is intrinsic to the KS dynamics since it arises from the vanishing of the effective viscosity when evolving from its microscopic negative KS value, to ...