Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T15:51:08.131Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological selection in stratified fluids: an example from air–water systems

Published online by Cambridge University Press:  06 March 2014

R. Camassa ,
S. Chen ,
G. Falqui ,
G. Ortenzi  and
M. Pedroni
R. Camassa
Affiliation:
University of North Carolina at Chapel Hill, Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Chapel Hill, NC 27599, USA
S. Chen
Affiliation:
University of North Carolina at Chapel Hill, Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Chapel Hill, NC 27599, USA
G. Falqui
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Milano, Italy
G. Ortenzi*
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Milano, Italy
M. Pedroni
Affiliation:
Dipartimento di Ingegneria, Università di Bergamo, Dalmine (BG), Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Topologically non-trivial configurations of stratified fluid domains are shown to generate selection mechanisms for conserved quantities. This is illustrated within the special case of a two-fluid system when the density of one of the fluids limits to zero, such as in the case of air and water. An explicit example is provided, demonstrating how the connection properties of the air domain affect total horizontal momentum conservation, despite the apparent translational invariance of the system. The correspondence between this symmetry and the selection process is also studied within the framework of variational principles for stratified ideal fluids.

JFM classification

Waves/Free-surface Flows: Channel flow Mathematical Foundations: Mathematical Foundations Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 743 , 25 March 2014 , pp. 534 - 553
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahamsen, B. C. & Faltinsen, O. M. 2011 The effect of air leakage and heat exchange on the decay of entrapped air pocket slamming oscillations. Phys. Fluids 23, 102107.Google Scholar
Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H. & Welcome, M. L. 1998 A conservative adaptive projection method for the variable density incompressible Navier–Stokes equations. J. Comput. Phys. 142, 1–46.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Benjamin, T. B. 1986 On the Boussinesq model for two-dimensional wave motions in heterogeneous fluids. J. Fluid Mech. 165, 445–474.CrossRefGoogle Scholar
Bidone, G.1820 Experiénces sur le remou et sur la propagation des ondes. Mem. de l’Acad. Royale des Sciences de Turin, Tome XXV.Google Scholar
Camassa, R., Chen, S., Falqui, G., Ortenzi, G. & Pedroni, M. 2012 An inertia ‘paradox’ for incompressible stratified Euler fluids. J. Fluid Mech. 695, 330–340.Google Scholar
Camassa, R., Chen, S., Falqui, G., Ortenzi, G. & Pedroni, M. 2013 Effects of inertia and stratification in incompressible ideal fluids: pressure imbalances by rigid confinement. J. Fluid Mech. 726, 404–438.Google Scholar
Carr, M., King, S. E. & Dritschel, D. G. 2012 Instability in internal solitary waves with trapped cores. Phys. Fluids 24, 016601.Google Scholar
Craig, W. & Sulem, C. 1993 Numerical simulation of gravity waves. J. Comput. Phys. 108, 73–83.CrossRefGoogle Scholar
Howard, L. N. & Yu, J. 2007 Normal modes of a rectangular tank with corrugated bottom. J. Fluid Mech. 593, 209–234.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Morrison, P. J. 1998 Hamiltonian description of the ideal fluid. Rev. Mod. Phys. 70, 467–521.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1989 Pouring flows with separation. Phys. Fluids A 1, 156–158.Google Scholar
Zakharov, V. E. & Kuznetsov, E. A. 1997 Hamiltonian formalism for nonlinear waves. Phys. Usp. 40, 1087–1116.CrossRefGoogle Scholar
Zakharov, V. E., Musher, S. L. & Rubenchik, A. M. 1985 Hamiltonian approach to the description of nonlinear plasma phenomena. Phys. Rep. 129, 285–366.Google Scholar