Transition to Condensate Formation in a Thin Rotating Fluid Layer

Two-dimensional (2d) and quasi-2d flows occur at macro- and mesoscale in a
variety of physical systems. Examples include stratified layers in Earth's
atmosphere and the ocean, soap films and more recently also in dense bacterial
suspensions, where the collective motion of microswimmers induces patterns of
mesoscale vortices. A characteristic feature of turbulence in 2d and thin fluid
layers is the occurrence of an inverse energy cascade. In case of weak
large-scale friction the inverse energy cascade results in the formation of
large-scale coherent structures, so-called condensates, which can take the form
of jets or large-scale vortices. With a view towards atmospheric physics, we
study the formation of the condensate in a rotating thin layer with free-slip
boundary conditions as function of the amplitude of the forcing, and we
quantify the effect of large-scale friction. Direct numerical simulations show
that the condensate appears in a first-order non-equilibrium phase transition,
with rare transitions occurring towards and away from the condensate state.
This clearly distinguishes between 2d dynamics and that of thin fluid layers, as
condensate formation 2d turbulence proceeds by means of a second-order
non-equilibrium phase transition.