The interplay between incompressibility and stratification can lead to non-conservation of horizontal momentum in the dynamics of a stably stratified incompressible Euler fluid filling an infinite horizontal channel between rigid upper and lower plates. Lack of conservation occurs even though in this configuration only vertical external forces act on the system. This apparent paradox was seemingly first noticed by Benjamin (J. Fluid Mech., vol. 165, 1986, pp. 445-474) in his classification of the invariants by symmetry groups with the Hamiltonian structure of the Euler equations in twodimensional settings, but it appears to have been largely ignored since. By working directly with the motion equations, the paradox is shown here to be a consequence of the rigid lid constraint coupling through incompressibility with the infinite inertia of the far ends of the channel, assumed to be at rest in hydrostatic equilibrium. Accordingly, when inertia is removed by eliminating the stratification, or, remarkably, by using the Boussinesq approximation of uniform density for the inertia terms, horizontal momentum conservation is recovered. This interplay between constraints, action at a distance by incompressibility, and inertia is illustrated by layer-averaged exact results, two-layer long-wave models, and direct numerical simulations of the incompressible Euler equations with smooth stratification. © Cambridge University Press 2012.

Camassa, R., Chen, S., Falqui, G., Ortenzi, G., Pedroni, M. (2012). An inertia 'paradox' for incompressible stratified Euler fluids. JOURNAL OF FLUID MECHANICS, 695, 330-340 [10.1017/jfm.2012.23].

An inertia 'paradox' for incompressible stratified Euler fluids

FALQUI, GREGORIO;ORTENZI, GIOVANNI;
2012

Abstract

The interplay between incompressibility and stratification can lead to non-conservation of horizontal momentum in the dynamics of a stably stratified incompressible Euler fluid filling an infinite horizontal channel between rigid upper and lower plates. Lack of conservation occurs even though in this configuration only vertical external forces act on the system. This apparent paradox was seemingly first noticed by Benjamin (J. Fluid Mech., vol. 165, 1986, pp. 445-474) in his classification of the invariants by symmetry groups with the Hamiltonian structure of the Euler equations in twodimensional settings, but it appears to have been largely ignored since. By working directly with the motion equations, the paradox is shown here to be a consequence of the rigid lid constraint coupling through incompressibility with the infinite inertia of the far ends of the channel, assumed to be at rest in hydrostatic equilibrium. Accordingly, when inertia is removed by eliminating the stratification, or, remarkably, by using the Boussinesq approximation of uniform density for the inertia terms, horizontal momentum conservation is recovered. This interplay between constraints, action at a distance by incompressibility, and inertia is illustrated by layer-averaged exact results, two-layer long-wave models, and direct numerical simulations of the incompressible Euler equations with smooth stratification. © Cambridge University Press 2012.
Articolo in rivista - Articolo scientifico
channel flow, general fluid mechanics, stratified flows
English
2012
695
330
340
none
Camassa, R., Chen, S., Falqui, G., Ortenzi, G., Pedroni, M. (2012). An inertia 'paradox' for incompressible stratified Euler fluids. JOURNAL OF FLUID MECHANICS, 695, 330-340 [10.1017/jfm.2012.23].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/31546
Citazioni
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
Social impact