Inter-cluster spacing in the infinite-domain limit of globally coupled systems

Determine whether, in the globally coupled version of the extended Ahmed–Neelin (2019) moisture model for convective self-aggregation—where every atmospheric column is equally coupled via the weak temperature gradient approximation—the inter-cluster distance diverges as the computational domain size tends to infinity, i.e., whether the preferred wavelength approaches infinity in the infinite-domain limit.

Background

In the numerical experiments, the globally coupled configuration yields a single moist cluster per periodic domain, implying that the observed inter-cluster distance is constrained by the finite domain size. This raises the question of how the characteristic spacing behaves as the domain grows without bound.

Because direct numerical exploration of the infinite-domain limit is infeasible, the authors flag this behavior as uncertain at this stage and motivate a later theoretical analysis of the steady-state structure using a dynamical-systems approach.