An atmospheric-pressure DBD in argon is investigated by means of time-dependent and spatially two-dimensional fluid-Poisson modelling in an axisymmetric geometry. The object of interest was formation of the striations along the discharge channel. The model comprises a set of balance equations for the particle number densities of electrons and the most important argon species (atomic Ar+ and molecular Ar2+ ions, as well as the lumped excited atomic Ar∗ and molecular Ar2∗ states of argon), Poisson’s equation for the electric potential and field, the electron energy balance equation and a balance equation for the surface charge density. The quasi-neutral initial conditions and physically-based boundary conditions, accounting for thermal flux and partial reflection of the particles, are used. The additional term describing the ion-induced emission of secondary electrons is included into the boundary conditions for the balance equations for the particle number density and energy density of electrons. The analysis of the spatiotemporal evolution of the particle species, electric field, mean electron energy and rates of electron production after reaching the quasi-periodic state was performed to determine the origin of the striations. The voltage and electric current, as well as the number densities, electric field and electron production rates were exported using LiveLink™ for MATLAB® (https://www.comsol.com/livelink-for-matlab) and post-processed using python3 (https://www.python.org) and Matplotlib (https://matplotlib.org).