  We study structure formation in two-dimensional turbulence driven by an
external force, interpolating between linear instability forcing and random
stirring, subject to nonlinear damping. Using extensive direct numerical
simulations, we uncover a rich parameter space featuring four distinct branches
of stationary solutions: large-scale vortices, hybrid states with embedded
shielded vortices (SVs) of either sign, and two states composed of many similar
SVs. Of the latter, the first is a dense vortex gas where all SVs have the same
sign and diffuse across the domain. The second is a hexagonal vortex crystal
forming from this gas when the instability is sufficiently weak. These
solutions coexist stably over a wide parameter range. The late-time evolution
of the system from small-amplitude initial conditions is nearly self-similar,
involving three phases: initial inverse cascade, random nucleation of SVs from
turbulence and, once a critical number of vortices is reached, a phase of
explosive nucleation of SVs, leading to a statistically stationary state. The
vortex gas is continued in the forcing parameter, revealing a sharp transition
towards the crystal state as the forcing strength decreases. This transition is
analysed in terms of the diffusion of individual vortices and tools from
statistical physics. The crystal can also decay via an inverse cascade
resulting from the breakdown of shielding or insufficient nonlinear damping
acting on SVs. Our study highlights the importance of the forcing details in
two-dimensional turbulence and reveals the presence of nontrivial SV states in
this system, specifically the emergence and melting of a vortex crystal.
