Physics – Fluid Dynamics
Scientific paper
2011-12-15
Physics
Fluid Dynamics
Scientific paper
10.1017/jfm.2012.23
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 two dimensional 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.
Camassa Roberto
Chen Shengqian
Falqui Gregorio
Ortenzi Giovanni
Pedroni Marco
No associations
LandOfFree
An inertia 'paradox' for incompressible stratified Euler fluids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An inertia 'paradox' for incompressible stratified Euler fluids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An inertia 'paradox' for incompressible stratified Euler fluids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-136072