NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (5), P. 854–864
On direct and inverse spectral problems for sloshing of a two-layer fluid in an open container
N. G. Kuznetsov – Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V. O., Bol’shoy pr. 61, St. Petersburg, 199178, Russian Federation; firstname.lastname@example.org
We study the direct and inverse eigenvalue problems for a pair of harmonic functions with a spectral parameter in boundary and coupling conditions. The direct problem is relevant to sloshing frequencies of free oscillations of a two-layer fluid in a container. The upper fluid occupies a layer bounded above by a free surface and below by a layer of fluid of greater density. Both fluids are assumed to be inviscid, incompressible, and heavy, whereas the free surface and the interface between fluids are considered bounded.
Keywords: Laplace equation, sloshing problem, two-layer fluid, eigenvalue, eigenfunction, inverse spectral problem.
PACS 02.30.Jr, 47.35.Bb