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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: giovanni.ortenzi@unimib.it
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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 

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