Numerical simulation of an obliquely incident solitary wave

Барахнин, В. Б.; Khakimzyanov, G. S.

doi:10.1007/bf02469167

Cited by 3 publications

(10 citation statements)

References 8 publications

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“…Longuet-Higgins & Fenton 1974). A similar numerical study was conducted by Barakhnin & Khakimzyanov (1999) and it was found that the values of ψ r , ψ w and α r are well predicted by Miles's theory with small amplitude, a i = 0.05, but not stem amplification, α w .…”

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confidence: 60%

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On the Mach reflection of a solitary wave: revisited

Yeh

Kodama

2011

J. Fluid Mech.

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Reflection of an obliquely incident solitary wave at a vertical wall is studied experimentally in the laboratory wave tank. Precision measurements of water-surface variations are achieved with the aid of laser-induced fluorescent (LIF) technique and detailed features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is not in the form of a Korteweg–de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression. Evolution of stem-wave amplification is in good agreement with the Kadomtsev–Petviashvili (KP) theory. The asymptotic characteristics and behaviours are also in agreement with the theory of Miles (J. Fluid Mech., vol. 79, 1977b, p. 171) except those in the neighbourhood of the transition between the Mach reflection and the regular reflection. The predicted maximum fourfold amplification of the stem wave is not realized in the laboratory environment. On the other hand, the laboratory observations are in excellent agreement with the previous numerical results of the higher-order model of Tanaka (J. Fluid Mech., vol. 248, 1993, p. 637). The present laboratory study is the first to sensibly analyse validation of the theory; note that substantial discrepancies exist from previous (both numerical and laboratory) experimental studies. Agreement between experiments and theory can be partially attributed to the large-distance measurements that the precision laboratory apparatus is capable of. More important, to compare the laboratory results with theory, the corrected interaction parameter is derived from proper interpretation of the theory in consideration of the finite incident wave angle. Our laboratory data indicate that the maximum stem wave can reach higher than the maximum solitary wave height. The wave breaking near the wall results in the substantial increase in wave height and slope away from the wall.

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supporting

confidence: 60%

“…On the other hand, previous laboratory experiments failed to verify Miles's theory, and so did the higher-order numerical simulations by Tanaka (1993) and Barakhnin & Khakimzyanov (1999); the observed or simulated features and behaviours do not match the theoretical predictions.…”

Section: On Incident Wave Angle ψ Imentioning

confidence: 78%

On the Mach reflection of a solitary wave: revisited

Yeh

Kodama

2011

J. Fluid Mech.

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“…These properties of the (3142)-type solution are the same as those of Miles's asymptotic solution for the Mach reflection of a shallow water soliton [22]. However one should note that the [1,4]-soliton corresponding to the Mach stem becomes a soliton solution only in an asymptotic sense. Then the exact solution of (3142)-type can provide an estimate of a propagation distance, at which the amplitude is sufficiently developed.…”

Section: The Mach Reflection and The Kp Solutionsmentioning

confidence: 53%

“…As was shown in [3], [4], each τ -function (16) generates a soliton solution which consists of at most two line-solitons for both y → ±∞. We consider the following two types which are relevant to the solutions of the initial value problems for the Mach reflection: one consists of two line-solitons of [1,2] and [3,4] for both |Y | 0, which is called O-type soliton ("O" stands for original, see [16], [4]); the other one consists of [1,3] and [3,4] line-solitons for Y 0 and [1,2] and [2,4] line-solitons for Y 0. Let us call this soliton (3142)-type, because those four line-solitons represent a permutation π = 1 2 3 4 3 1 4 2 .…”

Section: The Mach Reflection and The Kp Solutionsmentioning

confidence: 98%

“…A [3,4] = A [1,2] = 1 2 tan 2 ψ 0 < A 0 , and the angles of those in the negative x-regions do not depend on ψ 0 and ψ [3,4] = −ψ [1,2] = ψ c . Two sets of three solitons { [1,3], [1,4], [3,4]} and { [2,4], [1,4], [1,2]} are both in the soliton resonant state. These properties of the (3142)-type solution are the same as those of Miles's asymptotic solution for the Mach reflection of a shallow water soliton [22].…”

Section: The Mach Reflection and The Kp Solutionsmentioning

confidence: 99%

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Mach reflection and KP solitons in shallow water

Yeh

Kodama

2010

Eur. Phys. J. Spec. Top.

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Reflection of an obliquely incident solitary wave onto a vertical wall is studied analytically and experimentally. We use the Kadomtsev-Petviashivili (KP) equation to analyze the evolution and its asymptotic state. Laboratory experiments are performed using the laser induced fluorescent (LIF) technique, and detailed features and amplifications at the wall are measured. We find that proper physical interpretation must be made for the KP solutions when the experimental results are compared with the theory under the assumptions of quasi-two dimensionality and weak nonlinearity. Due to the lack of physical interpretation of the theory, the numerical results were previously thought not in good agreement with the theory. With proper treatment, the KP theory provides an excellent model to predict the present laboratory results as well as the previous numerical results. The theory also indicates that the present laboratory apparatus must be too short to achieve the asymptotic state. The laboratory and numerical results suggest that the maximum of the predicted four-fold amplification would be difficult to be realized in the real-fluid environment. The reality of this amplification remains obscure.

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Finite difference methods for 2D shallow water equations with dispersion

Khakimzyanov

Fedotova

Gusev

et al. 2019

Russian Journal of Numerical Analysis and Mathematical Modelling

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Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

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Numerical simulation of an obliquely incident solitary wave

Cited by 3 publications

References 8 publications

On the Mach reflection of a solitary wave: revisited

On the Mach reflection of a solitary wave: revisited

Mach reflection and KP solitons in shallow water

Finite difference methods for 2D shallow water equations with dispersion

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