Evolution of surface waves of finite amplitude in field of inhomogeneous current

Bakhanov, V. V.; Kemarskaya, O. N.; Pozdnyakova, V.P.; Okomel’kova, I. A.; Shereshevsky, L.A.

doi:10.1109/igarss.1996.516418

Cited by 6 publications

(6 citation statements)

References 2 publications

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“…Results of all experiments show that the average value of surface wave amplitude variability withf=2 Hz is 21 % more than for surface waves with f=1.7 Hz. It confirms the result of theoretical calculations for nonlinear surface waves with a weak dependence of the value of a surface-wave amplitude variability on its wave vector [2]. Most interesting effect discovered in the experiment is the increase of the variability a with the increase of a,.…”

Section: Resultssupporting

confidence: 89%

“…Because of this the large attention is recently given to a development of models of surface-wave transformations above a non-uniform bottom topography. One of such models uses a transformation of wind waves in a field of a non-uniform flow above bottom roughnesses [ 1,2]. The basic flow can be caused, for example, by a tide, and its modulation by bottom roughnesses causes a variability of surface waves.…”

Section: Introductionmentioning

confidence: 99%

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Action of inhomogeneous currents on fields of elevations and slopes of water surface nonlinear waves

Bakhanov

Kazakov

Kemarskaya

1998

IGARSS '98. Sensing and Managing the Environment. 1998 IEEE International Geoscience and Remote Sensing. Symposium Proceedings.

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The variability of surface waves parameters in a field of streamlining of a submerged driven sphere is investigated in a laboratory tank. Various frequency and amplitude surface waves were generated by a wave maker at the wall of the tank from which sphere started its motion. Surface wave were absorbed by a wave absorber at the opposite wall of the tank. The elevations of the surface were recorded by a system of ultrasonic sensors, and surface slopes were recorded by the specially created video system. The modification of the surface wave field with increase of a distance from the wave maker was investigated. The most interesting discovered effect is that with the increase of the amplitude of the generated surface wave a variability of their parameters grows in the field of the inhomogeneous current. Calculations based on our modeled integro-differential equation for the complex amplitude of surface waves show that the offered theoretical model describes the transformation of nonlinear surface waves in a field of inhomogeneous currents quite well.

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Section: Resultssupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Action of inhomogeneous currents on fields of elevations and slopes of water surface nonlinear waves

Bakhanov

Kazakov

Kemarskaya

1998

IGARSS '98. Sensing and Managing the Environment. 1998 IEEE International Geoscience and Remote Sensing. Symposium Proceedings.

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“…Previous work with this approach to wave-current interactions includes Bakhanov et al (1996) which briefly introduces the O( 3 ) current-modified nonlinear Schrödinger equation in one horizontal dimension (with a sinusoidal current) and gives details of an example in two horizontal dimensions, with a submerged moving point dipole. Bakhanov et al (1997) compared results from the O( 3 ) equation to experiment, with initial findings that are encouraging.…”

Section: Introductionmentioning

confidence: 99%

The current-modified nonlinear Schrödinger equation

Stocker

Peregrine

1999

J. Fluid Mech.

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By comparison with both experimental and numerical data, Dysthe's (1979) O(ε4) modified nonlinear Schrödinger; equation has been shown to model the evolution of a slowly varying wavetrain well (here ε is the wave steepness). In this work, we extend the equation to include a prescribed, large-scale, O(ε2) surface current which varies about a mean value. As an introduction, a heuristic derivation of the O(ε3) current-modified equation, used by Bakhanov et al. (1996), is given, before a more formal approach is used to derive the O(ε4) equation. Numerical solutions of the new equations are compared in one horizontal dimension with those from a fully nonlinear solver for velocity potential in the specific case of a sinusoidal surface current, such as may be due to an underlying internal wave. The comparisons are encouraging, especially for the O(ε4) equation.

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“…where the group velocity of gravity-capillary waves propagating on top of a current is: A similar equation was derived in Ref. [12] for purely gravity waves (the rigorous derivation of such equation with the help of the asymptotic expansion method can be found in Rev. [5]).…”

Section: Derivation Of the Effective Gross-pitaevskii Equations For Wmentioning

confidence: 90%

Modeling of Bose–Einstein Condensation in a Water Tank

Rousseaux

Stepanyants

2018

Nonlinear Waves and Pattern Dynamics

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It is shown that surface waves propagating against the external current, slowly varying in the horizontal direction in deep water, are governed by the equation which is tantamount to the Gross-Pitaevskii equation modelling the mean-field dynamics of Bose-Einstein condensate. The repulsive or attractive sign of the cubic term in the Gross-Pitaevskii equation is controlled by the choice of the carrier wavelength of the surface waves, while the spatial variation of the current plays the role of the external potential in that equation. The current profile can be easily controlled in the experiments by small variation of the bottom profile, so that the corresponding effective potential in the Gross-Pitaevskii equation can be made in the form of a well or hump. It is shown that the phenomenon of the Bose-Einstein condensation can be effectively emulated in relatively simple laboratory setups for water waves. Generating perturbations with an appropriate carrier wavelength, one can create patterns in the form of trapped waves which correspond to pinned states of Gross-Pitaevskii equation with local potentials. The estimates demonstrate that the parameters of bottom profile, background current, and surface waves are quite accessible to laboratory experiments.

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Evolution of surface waves of finite amplitude in field of inhomogeneous current

Cited by 6 publications

References 2 publications

Action of inhomogeneous currents on fields of elevations and slopes of water surface nonlinear waves

Action of inhomogeneous currents on fields of elevations and slopes of water surface nonlinear waves

The current-modified nonlinear Schrödinger equation

Modeling of Bose–Einstein Condensation in a Water Tank

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