Trapped Modes in a Three-Layer Fluid

• Published in: Journal of marine science and application Vol. 17; no. 1; pp. 45 - 56
• Main Authors: Saha, Sunanda, Bora, Swaroop Nandan
• Format: Journal Article
• Language: English
• Published: Harbin Harbin Engineering University 01.03.2018; Springer Nature B.V; Department of Mathematics, Dayananda Sagar University, Bangalore 560100, India%Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781039, India
• Subjects: Circular cylinders; Computational fluid dynamics; Cylinders; Depth; Electrical Machines and Networks; Engineering; Fluid flow; Free surfaces; Geotechnical Engineering & Applied Earth Sciences; Hydrodynamics; Incompressible flow; Incompressible fluids; Interfaces; Machinery and Machine Elements; Modes; Offshore Engineering; Power Electronics; Ratios; Research Article; Submergence; Surface tension; Trapped waves; Wave number; Wavelengths; Multipoles; Cut-off value; Pycnoclines; Trapped mode; Three-layer fluid
• ISSN: 1671-9433; 1993-5048
• DOI: 10.1007/s11804-018-0005-9

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.