Accession Number:

AD0756218

Title:

Second-Harmonic Resonance in the Interaction of Capillary and Gravity Waves,

Descriptive Note:

Corporate Author:

VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG COLL OF ENGINEERING

Personal Author(s):

Report Date:

1972-12-01

Pagination or Media Count:

31.0

Abstract:

The method of multiple scales is used to derive equations governing the temporal and spatial variation for the amplitudes and phases of inviscid capillary-gravity traveling waves in the case of second harmonic resonance Wiltons ripples, but including the effects of near resonance, liquid depth, and pressure perturbations exerted by an external subsonic gas on the liquidgas interface. The spatial form of the equations shows that, below a critical gas velocity, energy is transferred between the fundamental and its first harmonic in keeping with the energy conservation law. However, the amplitude of the first harmonic decreases with gas velocity. Above the critical gas velocity, the gasliquid interface grows monotonically with distance. It is found that pure amplitude-modulated waves are possible only at perfect resonance. Pure phase-modulated, near-resonant waves are periodic, as the resonance forces a readjustment of the phases to produce perfect resonance. The effectiveness of the resonance in rippling the interface increases as the liquid depth decreases. Author

Subject Categories:

  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE