A gravity wave
consisting of a single elevation of finite amplitude
that propagates without change of form.
First described in 1844 by Scott Russell in a British Association Report, its existence is a result of a balance between nonlinearity, which tends to steepen the wave front
in consequence of the increase of wave speed
with amplitude, and dispersion
, which tends to spread the wave front as the wave speed of any spectral component decreases with increasing wavenumber
. Most extensively studied are solitary waves on the free surface
of a homogeneous, nonrotating fluid of finite depth
. Surface solitary waves are also the easiest to observe. However, there also exist internal solitary waves, as the balance between nonlinearity and dispersion may be possible in the absence of a free surface by virtue of any or all of stratification
, and rotation. See also envelope soliton
Miles, J. W. 1980. Solitary waves. Annu. Rev. Fluid Mech.. 12. 11–43.
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