Internal solitary waves near a turning point

Knickerbocker, C. J.; Newell, Alan C.

doi:10.1016/0375-9601(80)90830-0

Cited by 44 publications

(19 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kaup and Newell [1978] suggested that an ISW in water of variable depth could convert its polarity when passing through a transition region where the nonlinearity coefficient changes sign. Polarity conversions between depression and elevation ISWs have been verified by laboratory experiments and by numerical models [Knickerbocker and Newell, 1980;Helfrich and Melville, 1986].…”

Section: Introductionmentioning

confidence: 81%

See 1 more Smart Citation

Satellite observation of internal solitary waves converting polarity

Zhao

Klemas

Zheng

et al. 2003

Geophysical Research Letters

View full text Add to dashboard Cite

[1] On a SPOT-3 visible image over the South China Sea continental shelf, two contrasting signatures of internal solitary waves (ISWs) are observed: darker stripes leading brighter stripes in the lower part, and brighter stripes leading darker stripes in the upper part. The authors suggest that the contrasting patterns are caused by ISWs of different polarities. A packet of ISWs is observed in the process of converting polarity due to bottom shoaling, both in the propagation direction and in the transect direction. The evolution process can be obtained by transferring information from the spatial domain to the temporal domain. The conversion process starts with the original depression ISWs passing the 160 m isobath. The evolution process can be divided into two phases: the first is the broadening of the original depression waves and the second is the appearance of the new-born elevation waves. These two phases are verified using numerical simulation.

show abstract

Section: Introductionmentioning

confidence: 81%

“…In our case, there are two elevation waves created behind the original depression wave (Figure 1). The ISW evolution in this phase has been studied by numerical method several times [Knickerbocker and Newell, 1980;Liu et al, 1998;Vlasenko and Hutter, 2002].…”

Section: Conversion Processmentioning

confidence: 99%

Satellite observation of internal solitary waves converting polarity

Zhao

Klemas

Zheng

et al. 2003

Geophysical Research Letters

View full text Add to dashboard Cite

show abstract

“…formulated the eKdV equation for slowly varying topography (l/L = O(α), where L is the horizontal length scale of the topography) and computed numerical solutions for solitary waves of depression propagating over slope-shelf topography, finding qualitative agreement with the essential features of the numerical solution of Knickerbocker & Newell (1980). They also used the numerical solutions at the top of the shelf, along with the Miura transformation and inverse scattering theory (Ablowitz & Segur 1981), to determine the asymptotic solution on the shelf, especially the number and amplitudes of the solitary waves.…”

Section: Variable Topography or Stratificationmentioning

confidence: 87%

“…However, there is an important difference for internal waves, which is associated with the fact that the coefficient of the quadratic term may change sign at a "turning point," which in the two-layer case with a small density difference between the layers corresponds to the point where h 1 = h 2 . Knickerbocker & Newell (1980) considered the problem using a KdV equation with slowly varying coefficients and argued that as the solitary wave propagates up the slope it would develop a lengthening trailing shelf of opposite sign. On approaching the turning point, the solitary wave deformed and lengthened, then, on passing through the turning point, waves of elevation evolved from the trailing shelf.…”

Section: Variable Topography or Stratificationmentioning

confidence: 99%

Long Nonlinear Internal Waves

Helfrich

Melville

2006

Annu. Rev. Fluid Mech.

685

491

View full text Add to dashboard Cite

Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.

show abstract

“…The event of vanishing of the relevant coefficient or a change in its sign therefore leads to substantial rearrangement of the wave propagation in the vicinity of the vanishing location. A natural consequence is that an approaching soliton of, say, elevation will be transformed into a soliton of depression, and vice versa (Knickerbocker and Newell, 1980;Talipova et al, 1997;Grimshaw et al, 1999).…”

Section: Gardner Equations For Interfacial Displacementsmentioning

confidence: 99%

Propagation regimes of interfacial solitary waves in a three-layer fluid

Kurkina¹,

Kurkin²,

Rouvinskaya³

et al. 2015

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

show abstract

Internal solitary waves near a turning point

Cited by 44 publications

References 5 publications

Satellite observation of internal solitary waves converting polarity

Satellite observation of internal solitary waves converting polarity

Long Nonlinear Internal Waves

Propagation regimes of interfacial solitary waves in a three-layer fluid

Contact Info

Product

Resources

About