Domaines de Recherche:  Physique/Mécanique/Mécanique des fluides
 Physique/Physique mathématique
 Mathématiques/Physique mathématique
 Science non linéaire/Formation de Structures et Solitons [nlin.PS]
 Planète et Univers/Sciences de la Terre/Géomorphologie
 Physique/Physique/Dynamique des Fluides
 Sciences de l'ingénieur/Mécanique/Mécanique des fluides
 Science non linéaire/Systèmes Solubles et Intégrables [nlin.SI]
 Physique/Physique/Physique Générale
 Physique/Matière Condensée/Autre
 Physique/Physique des Hautes Energies  Théorie

Dernieres productions scientifiques :


Green–Naghdi dynamics of surface wind waves in finite depth
Auteur(s): Manna M., Latifi A., Kraenkel Roberto
(Article) Publié:
Fluid Dynamics Research, vol. 50 p.025514 (2018)
Ref HAL: hal01710924_v1
DOI: 10.1088/18737005/aaa739
Exporter : BibTex  endNote
Résumé: The Miles' quasi laminar theory of waves generation by wind in finite depth h is presented. In this context, the fully nonlinear Green–Naghdi model equation is derived for the first time. This model equation is obtained by the non perturbative Green–Naghdi approach, coupling a nonlinear evolution of water waves with the atmospheric dynamics which works as in the classic Miles' theory. A depthdependent and winddependent wave growth γ is drawn from the dispersion relation of the coupled Green–Naghdi model with the atmospheric dynamics. Different values of the dimensionless water depth parameter $\delta = \frac{gh}{U_1}$, with g the gravity and $U_1$ a characteristic wind velocity, produce two families of growth rate γ in function of the dimensionless theoretical waveage $c_0$: a family of γ with h constant and $U_1$ variable and another family of $\gamma$ with $U_1$ constant and $h$ variable. The allowed minimum and maximum values of $\gamma$ in this model are exhibited.



Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth
Auteur(s): Latifi A., Manna M., Montalvo P., Ruivo M.
(Article) Publié:
Journal Of Applied Fluid Mechanics, vol. 10 p.18291843 (2017)
Ref HAL: hal01653592_v1
DOI: 10.18869/acadpub.jafm.73.243.27597
Exporter : BibTex  endNote
Résumé: This work regards the extension of the Miles’ and Jeffreys’ theories of growth of windwaves in water of finite depth. It is divided in two major sections. The first one corresponds to the surface water waves in a linear regimes and the second one to the surface water waver considered in a weak nonlinear, dispersive and antidissipative regime. In the linear regime, we extend the Miles’ theory of wind wave amplification to finite depth. The dispersion relation provides a wave growth rate depending to depth. A dimensionless water depth parameter depending to depth and a characteristic wind speed, induces a family of curves representing the wave growth as a function of the wave phase velocity and the wind speed. We obtain a good agreementbetween our theoretical results and the data from the Australian Shallow Water Experiment as well as the data from the Lake George experiment. In a weakly nonlinear regime the evolution of wind waves in finitedepth is reduced to an antidissipative Kortewegde VriesBurgers equation and its solitary wave solution is exhibited. Antidissipation phenomenon accelerates the solitary wave and increases its amplitude whichleads to its blowup and breaking. Blowup is a nonlinear, dispersive and antidissipative phenomenon which occurs in finite time. A consequence of antidissipation is that any solitary waves’ adjacent planes of constants phases acquire different velocities and accelerations and ends to breaking which occurs in finite space and in a finite time prior to the blowup. It worth remarking that the theoretical amplitude growth breaking time are both testable in the usual experimental facilities. At the end, in the context of windforced waves in finite depth, the nonlinear Schr ̈odinger equation is derived and for weak wind inputs, the Akhmediev, Peregrine and KuznetsovMa breather solutions are obtained



Finite time blowup and breaking of solitary wind waves
Auteur(s): Manna M., Montalvo P., Kraenkel R. a.
(Article) Publié:
Physical Review E: Statistical, Nonlinear, And Soft Matter Physics, vol. 90 p.013006 (2014)
Texte intégral en Openaccess :
Ref HAL: hal01234956_v1
DOI: 10.1103/PhysRevE.90.013006
Exporter : BibTex  endNote
2 citations
Résumé: The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg–de Vries–Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blowup and breaking. Blowup occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blowup. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.



Growth of cuspate spits
Auteur(s): Bouchette Frederic, Manna M., Montalvo P., Nutz Alexis, Schuster Mathieu, Ghienne JeanFrancois
(Article) Publié:
Journal Of Coastal Research, vol. p.4752 (2014)
Ref HAL: hal01234952_v1
DOI: 10.2112/SI70009.1
Exporter : BibTex  endNote
2 citations
Résumé: The present work concerns cuspate spits: slightly symmetrical geomorphic features growing along the shoreline in shallow waters. We develop a new formulation for the dynamics of cuspate spits. Our approach relies on classical paradigms such as a conservation law to the shoreface scale and an explicit formula for alongshore sediment transport. We derive a nonlinear diffusion equation and a fully explicit solution for the growth of cuspate spits. From this general expression, we found interesting applications to quantify shoreline dynamics in the presence of cuspate spits. In particular, we point out a simple method for the datation of a cuspate spit given a limited number of input parameters. Furthermore, we develop a method to quantify the mean alongshore diffusivity along a shoreline perturbed by welldefined cuspate spits of known sizes. Finally, we introduce a formal relationship between the geometric characteristics (amplitude, length) of cuspate spits, which reproduce the selfsimilarity of these geomorphic features.



Growth of Cuspate Spits
Auteur(s): Bouchette Frédéric, Manna M., Montalvo P., Nutz Alexis, Schuster Mathieu, Ghienne JeanFrançois
Conference: 13th International Coastal Symposium (Durban, ZA, 20140413)
Texte intégral en Openaccess :
Ref HAL: hal01006569_v1
Exporter : BibTex  endNote
Résumé: The present work concerns cuspate spits: slightly symmetrical geomorphic features growing along the shoreline in shallow waters. We develop a new formulation for the dynamics of cuspate spits. Our approach relies on classical paradigms such as a conservation law to the shoreface scale and an explicit formula for alongshore sediment transport. We derive a nonlinear diffusion equation and a fully explicit solution for the growth of cuspate spits. From this general expression, we found interesting applications to quantify shoreline dynamics in the presence of cuspate spits. In particular, we point out a simple method for the datation of a cuspate spit given a limited number of input parameters. Furthermore, we develop a method to quantify the mean alongshore diffusivity along a shoreline perturbed by welldefined cuspate spits of known sizes. Finally, we introduce a formal relationship between the geometric characteristics (amplitude, length) of cuspate spits, which reproduce the selfsimilarity of these geomorphic features.

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