Summary
This work is concerned with the analysis of some models for gravity wave propagation in water of variable depth. Within this framework, particular emphasis is put on the model recently proposed by Green and Naghdi. A detailed comparison with widely accepted theories allows us to consider the model by Green and Naghdi essentially as a theory closely related to the approximation of shallow water. However, the greater generality of this model, outlined in the present paper, opens new prospects of the possibility of achieving more satis-factory results about gravity wave propagation.
Riassunto
In questo lavoro si esaminano alcuni modelli per la propagazione delle onde di gravità in acqua di profondità variabile. In tale contesto, particolare attenzione è rivolta al modello proposto recentemente da Green e Naghdi. Un confronto dettagliato con teorie largamente in uso permette di collocare tale modello nell'ambito delle teorie dell'acqua poco profonda. Fortunatamente, la maggior generalità del modello di Green e Naghdi, delineata in questo lavoro, apre nuove prospettive sulla possibilità di ottenere risultati più soddisfacenti per la propagazione di onde di gravità.
Резюме
Зта работа касается анализа некоторых моделей распространения гравитационных волн в воде с переменной толщиной. В рамках зтого подхода особое внимание уделяется модели, недавно предложенной Грином и Нагди. Подробное сравнение с обшепринятыми теориями позволяет рассмотреть модель Гпина и Нагди, как теорию, непосредственно связанную с приближением мелкой воды. однако обобшение зтой модели, предложенное в зтой, открывает новые возможности получения более удовлетворительных результатов, касаюшихся распространения гравитационных волн.
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Bampi, F., Morro, A. Gravity waves in water of variable depth. Il Nuovo Cimento C 1, 377–388 (1978). https://doi.org/10.1007/BF02507664
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DOI: https://doi.org/10.1007/BF02507664