Miles, John On Faraday resonance of a viscous liquid. (English) Zbl 0965.76019 J. Fluid Mech. 395, 321-325 (1999). Summary: The tri-diagonal determinant for Faraday resonance of a viscous liquid subject to an externally imposed vertical oscillation is expressed in terms of the surface-wave impedance of the liquid, and developed as a continued fraction to obtain a systematic sequence of analytical approximations for the threshold acceleration. The impedance is calculated for either a clean or a fully contaminated surface on the assumption that the capillary, gravitational and viscous length scales are small compared with the breadth and depth of the liquid. Finally, we construct limiting approximations for weak and strong viscosity. Cited in 8 Documents MSC: 76D33 Waves for incompressible viscous fluids Keywords:weak viscosity; tri-diagonal determinant; Faraday resonance; viscous liquid; vertical oscillation; surface-wave impedance; continued fraction; analytical approximations; threshold acceleration; strong viscosity PDFBibTeX XMLCite \textit{J. Miles}, J. Fluid Mech. 395, 321--325 (1999; Zbl 0965.76019) Full Text: DOI