Accession Number:

ADA250962

Title:

Evolution of Weakly Nonlinear Water Waves in the Presence of Viscosity and Surfactant

Descriptive Note:

Technical rept.

Corporate Author:

MICHIGAN UNIV ANN ARBOR DEPT OF AEROSPACE ENGINEERING

Report Date:

1989-08-14

Pagination or Media Count:

61.0

Abstract:

Amplitude evolution equations are derived for viscous gravity waves and for viscous capillary-gravity waves with surfactants in water of infinite depth. Multiple scales are used to describe the slow modulation of a wave packet, and matched asymptotic expansions are introduced to represent the viscous boundary layer at the free surface. The resulting dissipative nonlinear Schrodinger equations show that the largest terms in the damping coefficients are unaltered from previous linear results up to third order in the amplitude expansions. The modulational instability of infinite wavetrains of small but finite amplitude is studied analytically and computationally. For capillary-gravity waves a band of Weber numbers is found in which the linear analysis guarantees neutral stability in the absence of viscous dissipation. The corresponding spectral computation shows modulation features that represent a small-amplitude recurrence not directly related to the Benjamin-Feir instability.

Subject Categories:

  • Numerical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE