Scaling properties of weakly nonlinear coefficients in the Faraday problem

Skeldon, Anne C. and Porter, Jeffrey Brent (2011). Scaling properties of weakly nonlinear coefficients in the Faraday problem. "Physical Review E", v. 84 (n. 1); p. 16209. ISSN 1539-3755. https://doi.org/10.1103/PhysRevE.84.016209.

Description

Title: Scaling properties of weakly nonlinear coefficients in the Faraday problem
Author/s:
  • Skeldon, Anne C.
  • Porter, Jeffrey Brent
Item Type: Article
Título de Revista/Publicación: Physical Review E
Date: July 2011
Volume: 84
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Aeronaves y Vehículos Espaciales
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Interesting and exotic surface wave patterns have regularly been observed in the Faraday experiment. Although symmetry arguments provide a qualitative explanation for the selection of some of these patterns (e.g., superlattices), quantitative analysis is hindered by mathematical difficulties inherent in a time-dependent, free-boundary Navier-Stokes problem. More tractable low viscosity approximations are available, but these do not necessarily capture the moderate viscosity regime of the most interesting experiments. Here we focus on weakly nonlinear behavior and compare the scaling results derived from symmetry arguments in the low viscosity limit with the computed coefficients of appropriate amplitude equations using both the full Navier-Stokes equations and a reduced set of partial differential equations due to Zhang and Vinãls. We find the range of viscosities over which one can expect ?low viscosity? theories to hold. We also find that there is an optimal viscosity range for locating superlattice patterns experimentally?large enough that the region of parameters giving stable patterns is not impracticably small, yet not so large that crucial resonance effects are washed out. These results help explain some of the discrepancies between theory and experiment.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainESP2007-65221-EUnspecifiedUnspecifiedExperimentos fluidos vibrados en microgravedad
Government of SpainAYA2010-19081UnspecifiedUnspecifiedExperimentos fluidos vibrados en microgravedad

More information

Item ID: 53467
DC Identifier: http://oa.upm.es/53467/
OAI Identifier: oai:oa.upm.es:53467
DOI: 10.1103/PhysRevE.84.016209
Official URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.016209
Deposited by: Memoria Investigacion
Deposited on: 11 Feb 2019 11:42
Last Modified: 11 Feb 2019 11:42
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