  The recent work of Siegelman \& Young (PNAS, vol. 120(44), 2023, pp.
e2308018120) revealed two extreme states reached by the evolution of unforced
and weakly-damped two-dimensional turbulence above random rough topography,
separated by a critical kinetic energy $E_\#$. The low- and high-energy
solutions correspond to topographically-locked and roaming vortices, surrounded
by non-uniform and homogeneous background potential vorticity (PV),
respectively. However, we found that these phenomena are restricted to the
particular intermediate length scale where the energy was initially injected
into the system. Through simulations initialised by injecting the energy at
larger and smaller length scales, we found that the long-term state of
topographic turbulence is also dependent on the initial length scale and thus
the initial enstrophy. If the initial length scale is comparable with the
domain size, the long-term flow field resembles the minimum-enstrophy state
proposed by Bretherton \& Haidvogel (J. Fluid Mech., vol.78(1), 1976, pp.
129-154), with very few topographically-locked vortices; the long-term
enstrophy is quite close to the minimum value, especially when the energy is no
larger than $E_\#$. As the initial length scale becomes smaller, more vortices
nucleate and become more mobile; the long-term enstrophy increasingly deviates
from the minimum value. Simultaneously, the background PV tends to
homogenization, even if the energy is below $E_\#$. These results complement
the phenomenology of topographic turbulence documented by Siegelman \& Young,
by showing that the minimum-enstrophy and background PV homogenization states
can be adequately approached by large- and small-scale initial fields,
respectively, with relatively arbitrary energy.
