The evolution of a localized nonlinear wave of the Kelvin―Helmholtz instability with gravity

• Published in: Physics of fluids (1994) Vol. 24; no. 11
• Main Authors: ORAZZO, Annagrazia, HOEPFFNER, Jérôme
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.11.2012
• Subjects: Computational fluid dynamics; Density; Earth, ocean, space; Exact sciences and technology; External geophysics; Fluid flow; Fluids; Gravitation; Mathematical analysis; Navier-Stokes equations; Nonlinearity; Physics of the oceans; Sea-air exchange processes; Wave propagation; Kelvin Helmholtz instability; Wind effect; digital simulation; Modeling; Surface gravity wave; Non linear wave
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4767512

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes-this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.