Internal Solitary Waves

Grimshaw, Roger

doi:10.1007/0-306-48024-7_1

Cited by 131 publications

(130 citation statements)

References 41 publications

Supporting

Mentioning

124

Contrasting

Order By: Relevance

“…The propagation of small amplitude long waves in a stratified fluid consisting of a relatively thin layer overlying a very deep passive layer is described by the well-known Benjamin-Ono (BO) equation [1,2,8] ∂u ∂t + αu ∂u ∂x…”

Section: Introductionmentioning

confidence: 99%

“…Here, u(x, t) is the perturbation of a pycnocline (a layer with a constant density) and α and β are parameters which depend on the particular stratification (for details see [2,8]). The symbol ℘ denotes the principal value of the integral.…”

Section: Introductionmentioning

confidence: 99%

“…Another widely used model in many physical contexts has m = 2 and δ < 0. This corresponds to Reynolds dissipation, For non-integer m the correct interpretation of the term (−ik) m is [8]. This model is based on the empirical description of dissipation in a turbulent boundary layer.…”

Section: Introductionmentioning

confidence: 99%

“…This dependence on time can be calculated by means of asymptotic theory [5,8,24] which presumes that the soliton adiabatically varies with time, while retaining its shape. This asymptotic theory in essence reduces to an energy balance equation which describes the time dependence of the governing soliton parameter A.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Decay of Benjamin–Ono solitons under the influence of dissipation

2018

View full text Add to dashboard Cite

The adiabatic decay of Benjamin-Ono algebraic solitons is studied when the influence of various types of small dissipation and radiative losses due to large scale Coriolis dispersion are taken into consideration. The physically most important dissipations are studied, Rayleigh and Reynolds dissipation, Landau damping, dissipation in a laminar boundary layer and Chezy friction on a rough bottom. The decay laws for the soliton parameters, that is amplitude, velocity and width, are found in analytical form and are compared with the results of direct numerical modelling.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decay of Benjamin–Ono solitons under the influence of dissipation

2018

View full text Add to dashboard Cite

show abstract

“…Nonlinear spatially inhomogeneous waveguides give rise to a number of effects which are of interest by themselves, and also find important applications in such diverse fields as optical dispersion-decreasing fibers (DDF) [1] and natural waveguides for internal waves in the ocean with a shear-flow background [2]. It is easy to understand that most nontrivial effects take place in the vicinity of a critical point, where the waveguide's dispersion or nonlinear coefficient changes sign.…”

Section: Introductionmentioning

confidence: 99%

Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schrödinger equation

2000

View full text Add to dashboard Cite

We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrödinger equation in which the dispersion coefficient changes its sign from normal to anomalous. The model has direct applications to dispersion-decreasing nonlinear optical fibers, and to natural waveguides for internal waves in the ocean. It is found that, depending on the (conserved) energy and (nonconserved) "mass" of the initial pulse, four qualitatively different outcomes of the pulse transformation are possible: decay into radiation; self-trapping into a single soliton; formation of a breather; and formation of a pair of counterpropagating solitons. A corresponding chart is drawn on a parametric plane, which demonstrates some unexpected features. In particular, it is found that any kind of soliton(s) (including the breather and counterpropagating pair) eventually decays into pure radiation with the increase of the energy, the initial "mass" being kept constant. It is also noteworthy that a virtually direct transition from a single soliton into a pair of symmetric counterpropagating ones seems possible. An explanation for these features is proposed. In two cases when analytical approximations apply, viz., a simple perturbation theory for broad initial pulses, or the variational approximation for narrow ones, comparison with the direct simulations shows reasonable agreement.

show abstract

Observation of internal wave polarity conversion generated by a rising tide

Wang

Grimshaw

2015

Geophysical Research Letters

Self Cite

View full text Add to dashboard Cite

The observations reported here are based on time series of in situ observation data in Laoshan Bay off the Qingdao coast. A chain of thermistors (T‐chain) at a fixed location recorded a sequence of elevation internal waves followed by depression internal waves passing by over an elapsed time of about 1 h. This observed polarity conversion at a fixed location is caused by the vertical stratification variation mainly induced by the rising tide, which is believed to be the first reported observation of this kind. The process of an elevation internal wave train converting to a depression wave train is simulated using the variable‐coefficient extended Korteweg‐de Vries (veKdV) equation, which also provides a further comparison between theory and the reported observations.

show abstract

Internal Solitary Waves

Cited by 131 publications

References 41 publications

Decay of Benjamin–Ono solitons under the influence of dissipation

Decay of Benjamin–Ono solitons under the influence of dissipation

Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schrödinger equation

Observation of internal wave polarity conversion generated by a rising tide

Contact Info

Product

Resources

About