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A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity
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10.1063/1.4768530
/content/aip/journal/pof2/24/12/10.1063/1.4768530
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4768530

Figures

Image of FIG. 1.
FIG. 1.

Shear flow with Ω > 0 (waves propagating downstream).

Image of FIG. 2.
FIG. 2.

Shear flow with Ω < 0 (waves propagating upstream).

Image of FIG. 3.
FIG. 3.

Stability diagram in the -plane. S : stable, U : unstable.

Image of FIG. 4.
FIG. 4.

Temporal evolution of the normalized maximum amplitude of the envelope in the case of a simple recurrence for kh = ∞ : (solid line), (dashed-dotted line).

Image of FIG. 5.
FIG. 5.

Temporal evolution of the normalized maximum amplitude of the envelope in the case of a double recurrence for kh = ∞ : (solid line), (dashed-dotted line).

Image of FIG. 6.
FIG. 6.

Normalized maximum growth rate as a function of for kh = 1.40 (solid line), kh = 1.70 (dashed line), and kh = 3.14 (dashed-dotted line). γ0max is the maximum growth rate in the absence of shear current.

Image of FIG. 7.
FIG. 7.

Normalized maximum growth rate as a function of kh for (solid line), (dashed line), and (dashed-dotted line). γ0max is the maximum growth rate when kh = ∞.

Image of FIG. 8.
FIG. 8.

Normalized growth rate as a function of the perturbation wavenumber ℓ for kh = 2.0 and (solid line), (dashed line), (dotted-dashed line).

Image of FIG. 9.
FIG. 9.

Normalized growth rate as a function of the perturbation wavenumber ℓ for kh = ∞ and (solid line), (dashed line), (dotted-dashed line).

Image of FIG. 10.
FIG. 10.

Normalized instability bandwidth as a function of for kh = 1.5 (solid line), kh = 1.8 (dashed line), kh = ∞ (dotted-dashed line).

Image of FIG. 11.
FIG. 11.

Normalized Benjamin Feir Index as a function of kh for several values of : (solid line), (dashed line), (dotted-dashed line).

Image of FIG. 12.
FIG. 12.

Normalized Benjamin Feir Index as a function of kh for several values of : (solid line), (dashed line), (dotted-dashed line).

Tables

Generic image for table
Table I.

Comparison with results of Oikawa et al.:13 F is the Froude number. The first value is estimated from their figures whereas the second one corresponds to our computations with the vor-NLS equation. Froude number F is exactly with our notations.

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/content/aip/journal/pof2/24/12/10.1063/1.4768530
2012-12-13
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4768530
10.1063/1.4768530
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