Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces with the confining boundaries. When contact happens, we show that the model evolution can lead to the dependent variables developing singularities in finite time. The conditions and the nature of these singularities are illustrated in several cases, progressing from a single-layer homogeneous fluid with a constant-pressure free surface and flat bottom, to the case of a two-fluid system contained between two horizontal rigid plates, and finally, through numerical simulations, to the full Euler stratified system. These demonstrate the qualitative and quantitative predictions of the models within a set of examples chosen to illustrate the theoretical results.

Camassa, R., Falqui, G., Ortenzi, G., Pedroni, M., Thomson, C. (2019). Hydrodynamic Models and Confinement Effects by Horizontal Boundaries. JOURNAL OF NONLINEAR SCIENCE, 29(4), 1445-1498 [10.1007/s00332-018-9522-6].

Hydrodynamic Models and Confinement Effects by Horizontal Boundaries

Falqui, G;Ortenzi, G
;
Pedroni, M;
2019

Abstract

Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces with the confining boundaries. When contact happens, we show that the model evolution can lead to the dependent variables developing singularities in finite time. The conditions and the nature of these singularities are illustrated in several cases, progressing from a single-layer homogeneous fluid with a constant-pressure free surface and flat bottom, to the case of a two-fluid system contained between two horizontal rigid plates, and finally, through numerical simulations, to the full Euler stratified system. These demonstrate the qualitative and quantitative predictions of the models within a set of examples chosen to illustrate the theoretical results.
Articolo in rivista - Articolo scientifico
Boundary-interface contact; Channel flows; Stratified fluids; Two-layer models; Modeling and Simulation; Engineering (all); Applied Mathematics
English
2019
29
4
1445
1498
partially_open
Camassa, R., Falqui, G., Ortenzi, G., Pedroni, M., Thomson, C. (2019). Hydrodynamic Models and Confinement Effects by Horizontal Boundaries. JOURNAL OF NONLINEAR SCIENCE, 29(4), 1445-1498 [10.1007/s00332-018-9522-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/223376
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