Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz equation
type: Item
instance of: scholarly article
title: Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz equation
zbMATH Open document ID: 0606.76015
DOI: 10.1155/S0161171286000200
author: B. N. Mandal
author: Rathindra Nath Chakrabarti
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46126
review text: Consider a two-fluid medium, both fluids being inviscid and incompressible. The mean surface of separation is taken as the x-z plane. A line source is present in either fluid such that the singular point is located at (0,\(\eta)\) or (0,-\(\eta)\) \((\eta >0)\). The strength of the source varies sinusoidally with time and z. The motion is assumed irrotational and of small amplitude. The problem is decomposed into two boundary value problems. Using the solution of the Laplacians as the intermediate stage, the potential is obtained. Cases of wave sources and finite depth of the lower fluid are considered as also the requirement of an out-going wave solution. The limiting situations of a static potential in a one fluid medium and of a time harmonic line source in a two fluid medium are indicated.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 3980714
zbMATH Keywords: surface waves
zbMATH Keywords: Helmholtz problem
zbMATH Keywords: mean surface
zbMATH Keywords: separation
zbMATH Keywords: line source
zbMATH Keywords: singular point
zbMATH Keywords: boundary value problems
zbMATH Keywords: wave sources
zbMATH Keywords: out-going wave solution
zbMATH Keywords: static potential
zbMATH Keywords: time harmonic line source
reviewed by: E. S. R. Gopal
MaRDI profile type: Publication
OpenAlex ID: W2058052764
description: scientific article; zbMATH DE number 3980714