Exact solution of the wave-resistance problem for a submerged cylinder. I: Linearized theory
type: Item
instance of: scholarly article
title: Exact solution of the wave-resistance problem for a submerged cylinder. I: Linearized theory
zbMATH Open document ID: 0998.76010
author: Dario Pierotti
author: Carlo D. Pagani
published in: Archive for Rational Mechanics and Analysis
publication date: 2002-11-24T00:00:00Z
review text: The authors consider two-dimensional fluid in an infinite channel with free surface and a submerged obstacle of finite length and small thickness. Looking for a steady, inviscid and irrotational flow, the authors expand the nonlinear problem in powers of the thickness of the obstacle. To leading order, they derive a linear elliptic equation in a strip, cut along a horizontal line segment in the interior, and equipped with certain (linear) boundary conditions on both sides of the cut and on the top and bottom of the strip. Subtracting a harmonic function which satisfies the given boundary conditions, the authors reduce the original problem to a Dirichlet problem in an infinite strip without cut. This problem is then solved using a variational characterization of the solution. The result is an essential ingredient to the solution of the nonlinear problem examined in part II [see the following entry].
reviewed by: Arnd Scheel
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76M45
zbMATH DE Number: 1419581
zbMATH Keywords: thin obstacle
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: strip with cut
zbMATH Keywords: variational method
zbMATH Keywords: linear boundary conditions
zbMATH Keywords: steady inviscid irrotational flow
zbMATH Keywords: two-dimensional fluid
zbMATH Keywords: infinite channel
zbMATH Keywords: free surface
zbMATH Keywords: submerged obstacle
zbMATH Keywords: linear elliptic equation
zbMATH Keywords: harmonic function
zbMATH Keywords: Dirichlet problem
MaRDI profile type: Publication
full work available at URL: s002050050175
OpenAlex ID: W2091943708
DOI: 10.1007/S002050050175
description: scientific article; zbMATH DE number 1419581