1980
DOI: 10.1016/0375-9601(80)90830-0
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Internal solitary waves near a turning point

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Cited by 44 publications
(19 citation statements)
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“…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
“…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%
“…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%
“…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%
“…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%