Asymmetric flexuralgravity lumps in nonuniform media
Abstract
Here we show that asymmetric fully localized flexuralgravity lumps can propagate on the surface of an inviscid and irrotational fluid covered by a variablethickness elastic material, provided that the thickness varies only in one direction and has a local minimum. We derive and present equations governing the evolution of the envelope of flexuralgravity wave packets allowing the flexing material to have small variations in the transverse (to propagation) direction. We show that the governing equation belongs to the general family of DaveyStewartson equations, but with an extra term in the surface evolution equation that accounts for the variable thickness of the elastic cover. We then use an iterative NewtonRaphson scheme, with a numerical continuation procedure via Lagrange interpolation, in a search to find fully localized solutions of this system of equations. We show that if the elastic sheet thickness has (at least) a local minimum, flexuralgravity lumps can propagate near the minimum thickness, and in general have an asymmetric bellshape in the transverse to the propagation direction. In applied physics, flexuralgravity waves describe for instance propagation of waves over the icecovered bodies of water. Ice is seldom uniform, nor is the seafloor, and in fact near the boundaries (iceedges, shorelines) they typically vary only in one direction (toward to edge), and are uniform in the transverse direction. This research suggests that fully localized waves are not restricted to constant icethickness/waterdepth areas and can exist under much broader conditions. Presented results may have implications in experimental generation and observation of flexuralgravity (as well as capillarygravity) lumps.
 Publication:

Physics of Fluids
 Pub Date:
 September 2014
 DOI:
 10.1063/1.4895017
 arXiv:
 arXiv:1403.0043
 Bibcode:
 2014PhFl...26i2105L
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 doi:10.1063/1.4895017