  Dark matter substructures emerge naturally in a scenario in which the axion
angular field acquires propagating degrees of freedom in a post-inflationary
Universe. The DALI experiment is a new generation wavy dark matters
interferometer currently in prototyping. Although DALI's main objective is to
explore the virialized DM in our Galaxy, to a large degree in this article we
explore the prospect for detection of fine grained streams made of axions that
would enter the Solar System, as suggested by previous work. We find that DALI
will have a sensitivity to encounters with these coherent objects that fully
spans the window defined by the coupling strength to photons of representative
axion models over a stacked bandwidth of two decades in mass.
