Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

Details Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

Mar 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999stin...0104361k&link_type=abstract

Proceedings of the Fourth Microgravity Fluid Physics and Transport Phenomena Conference, p. 477

Physics

Viscous Flow, Flow Stability, Oscillating Flow, Annular Flow, Liquid Bridges, Capillary Flow, Nonlinearity, Vortices, Faraday Effect, Vibration

Scientific paper

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h3))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

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