Editing Capillary waves
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This derivation makes clear the assumptions introduced. In particular, the linearization will only hold for smooth waves, the ones for which the wave amplitude, <math>a</math> is smaller than the wavelength. Mathematically, the limit is <math>q a \ll 1</math>. For ocean waves, this happens when waves approach the shore and the amplitude grows (in this limit, a bottom boundary condition <math>v_z (z=-H) =0</math> must be employed, and waves are not dispersive, see Ref 7.) | This derivation makes clear the assumptions introduced. In particular, the linearization will only hold for smooth waves, the ones for which the wave amplitude, <math>a</math> is smaller than the wavelength. Mathematically, the limit is <math>q a \ll 1</math>. For ocean waves, this happens when waves approach the shore and the amplitude grows (in this limit, a bottom boundary condition <math>v_z (z=-H) =0</math> must be employed, and waves are not dispersive, see Ref 7.) | ||
==External links== | |||
*[http://en.wikipedia.org/wiki/Capillary_wave Capillary wave entry in wikipedia] | |||
*[http://en.wikipedia.org/wiki/Thermal_capillary_wave Thermal capillary wave entry in wikipedia] | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1103/PhysRevLett.15.621 F. P. Buff, R. A. Lovett, and F. H. Stillinger, Jr. "Interfacial density profile for fluids in the critical region" Physical Review Letters '''15''' pp. 621-623 (1965)] | #[http://dx.doi.org/10.1103/PhysRevLett.15.621 F. P. Buff, R. A. Lovett, and F. H. Stillinger, Jr. "Interfacial density profile for fluids in the critical region" Physical Review Letters '''15''' pp. 621-623 (1965)] | ||
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#R.P. Feynman, R.B. Leighton, and M. Sands "The Feynman lectures on physics" Addison-Wesley 1963. Section 51-4. ISBN 0201021153 | #R.P. Feynman, R.B. Leighton, and M. Sands "The Feynman lectures on physics" Addison-Wesley 1963. Section 51-4. ISBN 0201021153 | ||
#[http://dx.doi.org/10.1006/rwos.2001.0129 W.K. Melville "Surface, gravity and capillary waves"], in [http://www.sciencedirect.com/science/referenceworks/9780122274305 "Encyclopedia of Ocean Sciences"], Eds: Steve A. Thorpe and Karl K. Turekian. Elsevier 2001, page 2916. ISBN 978-0-12-227430-5 | #[http://dx.doi.org/10.1006/rwos.2001.0129 W.K. Melville "Surface, gravity and capillary waves"], in [http://www.sciencedirect.com/science/referenceworks/9780122274305 "Encyclopedia of Ocean Sciences"], Eds: Steve A. Thorpe and Karl K. Turekian. Elsevier 2001, page 2916. ISBN 978-0-12-227430-5 | ||
[[Category: Classical thermodynamics ]] | |||
#[http://dx.doi.org/10.1088/0143-0807/25/1/014 F Behroozi "Fluid viscosity and the attenuation of surface waves: a derivation based on conservation of energy", European Journal of Physics '''25''' 115 (2004)] | #[http://dx.doi.org/10.1088/0143-0807/25/1/014 F Behroozi "Fluid viscosity and the attenuation of surface waves: a derivation based on conservation of energy", European Journal of Physics '''25''' 115 (2004)] | ||