  A two-field model of potential vorticity (PV) staircase structure and
dynamics relevant to both beta-plane and drift-wave plasma turbulence is
studied numerically and analytically. The model evolves averaged PV whose flux
is both driven by and regulates, a potential enstrophy field, $\varepsilon$.
The model employs a closure using a mixing length model. Its link to
bistability, vital to staircase generation, is analyzed and verified by
integrating the equations numerically. Long-time staircase evolution
consistently manifests a pattern of meta-stable quasi-periodic configurations,
lasting for hundreds of time units, yet interspersed with abrupt ($\Delta
t\ll1$) mergers of adjacent steps in the staircase. The mergers occur at the
staircase lattice defects where the pattern has not completely relaxed to a
strictly periodic solution that can be obtained analytically. Other types of
stationary solutions are solitons and kinks in the PV gradient and
$\varepsilon$ - profiles. The waiting time between mergers increases strongly
as the number of steps in the staircase decreases. This is because of an
exponential decrease in inter-step coupling strength with growing spacing. The
long-time staircase dynamics is shown numerically be determined by local
interaction with adjacent steps. Mergers reveal themselves through the
explosive growth of the turbulent PV-flux which, however, abruptly drops to its
global constant value once the merger is completed.
