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Title: The Stability of a Hydrodynamic Bravais Lattice
We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart.  more » « less
Award ID(s):
2154151
NSF-PAR ID:
10415302
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Symmetry
Volume:
14
Issue:
8
ISSN:
2073-8994
Page Range / eLocation ID:
1524
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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