scholarly journals Dispersive internal long wave models

1998 ◽  
Author(s):  
R. Camassa ◽  
W. Choi ◽  
D.D. Holm ◽  
C.D. Levermore ◽  
Y. Lvov
Keyword(s):  
Long Wave ◽  
Wave Models

Swash zone boundary conditions for long-wave models

2005 ◽  
Vol 52 (10-11) ◽  
pp. 971-976 ◽  
Author(s):  
Giorgio Bellotti ◽  
Maurizio Brocchini
Keyword(s):  
Boundary Conditions ◽  
Swash Zone ◽  
Zone Boundary ◽  
Long Wave ◽  
Wave Models

Nonlinear long-wave models for imperfectly bonded layered waveguides

2009 ◽  
Vol 159 (3) ◽  
pp. 819-832 ◽  
Author(s):  
K. R. Khusnutdinova ◽  
A. M. Samsonov ◽  
A. S. Zakharov
Keyword(s):  
Long Wave ◽  
Wave Models

On viscous film flows coating the interior of a tube: thin-film and long-wave models

2015 ◽  
Vol 772 ◽  
pp. 569-599 ◽  
Author(s):  
Roberto Camassa ◽  
H. Reed Ogrosky
Keyword(s):  
Thin Film ◽  
Numerical Solutions ◽  
Travelling Wave ◽  
Long Wave ◽  
Fluid Core ◽  
Primary Model ◽  
Long Time ◽  
Dynamical Regimes ◽  
Wave Models ◽  
Comparison Of The Results

A theoretical and numerical investigation of two classes of models for pressure-driven core–annular flow is presented. Both classes, referred to as ‘long-wave’ and ‘thin-film’ models, may be derived from a unified perspective using long-wave asymptotics, but are distinct from one another in the role played by the curved tube geometry with respect to the planar (limiting) case. Analytical and numerical techniques are used to show and quantify the significant differences between the behaviour of solutions to both model types. Temporal linear stability analysis of the constant solution is carried out first to pinpoint with closed-form mathematical expressions the different dynamical regimes associated with absolute or convective instabilities. Numerical simulations for the models are then performed and qualitative differences in the evolution of the free surface are explored. Mathematically, different levels of asymptotic accuracy are found to result in different regularizing properties affecting the long-time behaviour of generic numerical solutions. Travelling wave solutions are also studied, and qualitative differences in the topology of streamline patterns describing the flow of the film in a moving reference frame are discussed. These topological differences allow for further classification of the models. In particular, a transition from a regime in which waves trap a fluid core to one where waves travel faster than any parcel of the underlying fluid is documented for a variant of the primary model. In the corresponding thin-film model, no such transition is found to occur. The source of these differences is examined, and a comparison of the results with those of related models in the literature is given. A brief discussion of the merits of each class of models concludes this study.

Hamiltonian Formulation and Long Wave Models for Internal Waves

2007 ◽  
Author(s):  
Walter Craig ◽  
Philippe Guyenne ◽  
Henrik Kalisch
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Wave Equations ◽  
Hamiltonian Formulation ◽  
Solitary Wave Solutions ◽  
Free Interface ◽  
Wave Solutions ◽  
Long Wave ◽  
Wave Models ◽  
Upper Boundary

We derive a Hamiltonian formulation of the problem of a dynamic free interface (with rigid lid upper boundary conditions), and of a free interface coupled with a free surface, this latter situation occurring more commonly in experiment and in nature. Based on the linearized equations, we highlight the discrepancies between the cases of rigid lid and free surface upper boundary conditions, which in some circumstances can be significant. We also derive systems of nonlinear dispersive long wave equations in the large amplitude regime, and compute solitary wave solutions of these equations.

scholarly journals A Boussinesq type extension of the GeoClaw model - a study of wave breaking phenomena applying dispersive long wave models

2017 ◽  
Vol 122 ◽  
pp. 75-86 ◽  
Author(s):  
Jihwan Kim ◽  
Geir K. Pedersen ◽  
Finn Løvholt ◽  
Randall J. LeVeque
Keyword(s):  
Wave Breaking ◽  
Long Wave ◽  
Wave Models
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