Laboratory investigations of nonlinear surface wave transformation in a field of two-dimensionally inhomogeneous currents

Bakhanov, V. V.; Bogatyrev, S.D.; Kazakov, V. I.; Kemarskaya, O. N.

doi:10.1109/igarss.1997.615882

Cited by 1 publication

(4 citation statements)

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“…Also valuable would be a comparison of the results from our numerical calculations with those from experiments, as in Lo & Mei (1985) and Trulsen, Stansberg & Velarde (1999) for the case when no current is present, and as Bakhanov et al (1997) have done for the CNLS 3 equation. Another form of current that is of interest has shear in the vertical.…”

Section: Resultsmentioning

confidence: 98%

“…Further studies could follow the work of Trulsen & Dysthe (1996 to include the extra terms to make the equation valid for a broader bandwidth, and observe the nature of the frequency downshift in the presence of a current. Also valuable would be a comparison of the results from our numerical calculations with those from experiments, as in Lo & Mei (1985) and Trulsen, Stansberg & Velarde (1999) for the case when no current is present, and as Bakhanov et al (1997) have done for the CNLS 3 equation. Another form of current that is of interest has shear in the vertical.…”

Section: Resultsmentioning

confidence: 98%

“…Bakhanov et al (1997) compared results from the O( 3 ) equation to experiment, with initial findings that are encouraging. Trulsen & Dysthe (1996) extended the O( 4 ) MNLS equation to apply to waves with a broader bandwidth.…”

Section: Introductionmentioning

confidence: 97%

“…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. Trulsen & Dysthe (1996) extended the O( 4 ) MNLS equation to apply to waves with a broader bandwidth.…”

Section: Introductionmentioning

confidence: 97%

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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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Section: Resultsmentioning

confidence: 98%