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Effects of viscosity on water waves

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Il Nuovo Cimento C

Summary

The paper deals with the behaviour of a viscous liquid whose flow preserves the structure of the material columns. A balance law for energy is established which accounts for Navier-Stokes dissipation; on appealing to the invariance of such a low under rigid motions, balance equations for mass and linear momentum are derived. It is an outstanding consequence of the theory that the simultaneous occurence of viscosity and inertia terms makes long gravity waves be governed by the combined Korteweg-de Vries and Burgers equation.

Riassunto

Si considera il comportamento di un liquido viscoso il cui flusso conserva la struttura delle colonne materiali. Si formula un bilancio dell'energia che contiene il termine dissipativo di Navier-Stokes; applicando quindi l'invarianza di tale legge di bilancio per moti rigidi si deducono le leggi di bilancio per la massa e la quantità di moto. È una rilevante conseguenza della teoria che, per la simultanea presenza di termini inerziali e viscosità, le onde lunghe di gravità sono governate dall'equazione combinata di Korteweg-de Vries e Burgers.

Резюме

Рассматривается поведение вязкой жидкости, поток которой сохраняет структуру столба вешества. Формулируется баланс энергии, который содержит диссипативный член Навье-Стокса. Используя инвариантность этого закона относительно недформируемых движений, выводятся уравнения баланса для массы и импульса. Получено важное следствие зтой теории: одновременное появление членов, связанных с вязкостью и инерцией, приводит к что длинные гравитационные волны определяются объединенным уравнением Кортевега-де Вриса и ъургерса.

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Authors and Affiliations

  1. Istituto di Matematica dell' Università, Genova

    F. Bampi & A. Morro

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  1. F. Bampi
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  2. A. Morro
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Bampi, F., Morro, A. Effects of viscosity on water waves. Il Nuovo Cimento C 4, 551–562 (1981). https://doi.org/10.1007/BF02506958

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  • DOI: https://doi.org/10.1007/BF02506958

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