Trapped modes in a channel containing three layers of fluids and a submerged cylinder |
| |
Authors: | A Chakrabarti P Daripa Hamsapriye |
| |
Institution: | (1) Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India;(2) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;(3) Department of Haematology, Cambridge Institute of Medical Research, University of Cambridge, Wellcome Trust / MRCBuilding, Hills Road, Cambridge, CB2 2XY, U.K |
| |
Abstract: | The problem of existence of trapped waves in fluids due to a cylinder is investigated for the hydrodynamic set-up which involves
a horizontal channel of infinite length and depth and of finite width containing three layers of incompressible fluids of
different constant densities. The set-up also contains a cylinder which is impermeable, fully immersed in the bottom (lower-most)
fluid layer of infinite depth, and extends across the channel with its generators perpendicular to the side walls of the channel.
When the ratios of the densities of the adjacent fluids differ from unity by sufficiently small quantities, the underlying
mathematical problem reduces to a generalized nonlinear eigenvalue problem involving a cubic polynomial-cum-operator equation.
The perturbation analysis of this eigenvalue problem suggests existence of three distinct modes with different frequencies:
one of the order of one persisting at the free surface, and the other two of the order of the density ratio (except for modulo
one) persisting at the two internal interfaces. The correlation between these results for the three-layer case and very recent
numerical results of other authors in the two-layer case has also been addressed.
Received: March 3, 2005 |
| |
Keywords: | Trapped waves potential flows interfacial flows |
本文献已被 SpringerLink 等数据库收录! |
|