Viscous Effects on Small-Amplitude Surface Waves

Date

1976-02

Journal Title

Journal ISSN

Volume Title

Publisher

The Physics of Fluids

Abstract

The transient behavior of small?amplitude standing waves on the plane surface of an infinitely deep viscous liquid is investigated. An integro?differential equation of motion for the free surface is derived and solved exactly. The small?time behavior of the solution agrees with that computed in the approximation of irrotational flow, and the large?time one with the results for the discrete spectrum obtained by means of the standard normal?mode analysis. In between these two asymptotic regimes, however, the exact solution is significantly different from either approximation, except when the effect of viscosity is very small.

Description

Keywords

Integro-differential equation, Surface waves, Viscous liquid

Citation

Copyright 1976 The Physics of Fluids. Recommended citation: Prosperetti, Andrea. "Viscous effects on small?amplitude surface waves." The Physics of Fluids 19, no. 2 (1976): 195-203. DOI: 10.1063/1.861446 URL: https://aip.scitation.org/doi/abs/10.1063/1.861446 Reproduced in accordance with the original publisher’s licensing terms and with permission from the author(s).