We first consider the Lagrangian mechanics setting proposed by Darryl Holm and his collaborators, in which the evolutionary equations of internal waves can be obtained via the Euler-Poincare reduction technique, under the so-called columnar ´ motion ansatz assumption. Then, we go on explaining the classical model proposed by T. Wu and Camassa-Choi to formulate evolutionary equations of the internal waves, by means of Taylor-expansion in the vertical direction. Finally, based on the classical Hamiltonian formalism for 2D wave motions in heterogeneous fluids by Benjamin, we derive the Hamiltonian structure of 2-layer stratified fluids, with and without dispersion, under the Weakly Nonlinear and Mildly Nonlinear assumption.

Consideriamo dapprima l'impostazione della meccanica lagrangiana proposta da Darryl Holm ei suoi collaboratori, in cui possono essere le equazioni evolutive delle onde interne ottenuto mediante la tecnica di riduzione di Eulero-Poincare, sotto il cosiddetto colonnare ´ ipotesi di movimento ansatz. Proseguiamo quindi con la spiegazione del modello classico proposto da T. Wu e Camassa-Choi per formulare equazioni evolutive dell'interno onde, mediante espansione di Taylor in direzione verticale. Infine, in base a il classico formalismo hamiltoniano per moti ondulatori 2D in fluidi eterogenei da Benjamin, deriviamo la struttura hamiltoniana di fluidi stratificati a 2 strati, con e senza dispersione, sotto Debolmente Nonlineare e Lievemente Nonlineare assunzione.

(2023). Hamiltonian approach to 2-layer dispersive stratified fluids. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2023).

Hamiltonian approach to 2-layer dispersive stratified fluids

VU HO, THAO THUAN
2023

Abstract

We first consider the Lagrangian mechanics setting proposed by Darryl Holm and his collaborators, in which the evolutionary equations of internal waves can be obtained via the Euler-Poincare reduction technique, under the so-called columnar ´ motion ansatz assumption. Then, we go on explaining the classical model proposed by T. Wu and Camassa-Choi to formulate evolutionary equations of the internal waves, by means of Taylor-expansion in the vertical direction. Finally, based on the classical Hamiltonian formalism for 2D wave motions in heterogeneous fluids by Benjamin, we derive the Hamiltonian structure of 2-layer stratified fluids, with and without dispersion, under the Weakly Nonlinear and Mildly Nonlinear assumption.
FALQUI, GREGORIO
fluidi stratificati; struttura hamiltonia; approccio variaziona; fluidi dispersivi; meccanica lagrangian
stratified fluids; Hamiltonian structur; Lagrangian approach; dispersive fluids; variational approach
MAT/07 - FISICA MATEMATICA
English
5-mag-2023
35
2021/2022
open
(2023). Hamiltonian approach to 2-layer dispersive stratified fluids. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2023).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/414626
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