Projects per year
Abstract
This paper provides a new insight to the classical Björknes’s problem. We examine a mechanical system “solid+fluid” consisted of a solid and a point source (singlet) of fluid, whose intensity is a given function of time. First we show that this system is governed by the least action (Hamilton’s) principle and derive an explicit expression for the Lagrangian in terms of the Green function of the solid. The Lagrangian contains a linear in velocity term. We prove that it does not produce a gyroscopic force only in the case of a spherical solid. Then we consider the periodical highfrequency pulsations (vibrations) of the singlet. In order to construct the highfrequency asymptotic solution we employ a version of the multiple scale method that allows us to obtain the “slow” Lagrangian for the averaged motions directly from Hamilton’s principle. We derive such a “slow” Lagrangian for a general solid. In details, we study the “slow” dynamics of a spherical solid, which can be either homogeneous or inhomogeneous in density. Finally, we discuss the “Björknes’s dynamic buoyancy” for a solid of general form.
Original language  English 

Title of host publication  Regular and Chaotic Dynamics 
Subtitle of host publication  Hamiltonian Dynamics, Vortex Structures, Turbulence: Proceedings of the IUTAM Symposium held in Moscow, 25–30 August, 2006 
Editors  Alexey Borisov, Valery Kozlov, Ivan Mamaev, Mikhail Sokolovskiy 
Publisher  Springer 
Pages  135150 
Number of pages  15 
Volume  6 
ISBN (Electronic)  9781402067440 
ISBN (Print)  9781402067433 
DOIs  
Publication status  Published  2008 
Publication series
Name  IUTAM Bookseries 

Keywords
 Fluid Dynamics
Projects
 2 Finished


Stability of Inviscid flows through a given domain
1/03/06 → 29/02/08
Project: Research project (funded) › Research