Open AccessJournal Article10.1137/S0036139900372569

Bifurcation Analysis for Surface Waves Generated by Wind

- 01 Jan 2001

- Vol. 62, Iss: 2, pp 407-423

TL;DR: An asymptotic formula is derived for the average tangential velocity along the free surface of surface waves on water as a bifurcation phenomenon and it is found that for a critical wind-speed there appear traveling wave solutions.

Abstract: We study the generation of surface waves on water as a bifurcation phenomenon For a critical wind-speed there appear traveling wave solutions While linear waves do not transport mass (in the mean), nonlinear effects create a shear-flow and result in a net mass transport in the direction of the wind We derive an asymptotic formula for the average tangential velocity along the free surface Numerical investigations confirm the appearance of the shear-flow and yield results on the bifurcation picture

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1. What are the contributions in "Bifurcation analysis for surface waves generated by wind∗" ?

The authors study the generation of surface waves on water as a bifurcation phenomenon.

2. What have the authors stated for future works in "Bifurcation analysis for surface waves generated by wind∗" ?

Their aim is to study the effect of the nonlinear contributions in the bifurcation problem.. In this way the authors can get a better understanding of the bifurcation picture and find properties of the solutions that are not present in the linearized model.. The authors can now set ṽ = v ◦Θ, p̃ = p ◦Θ, with v: R → R2 and p: R → R.. The authors can now transform the above equation term by term.

Table 2 Tangential speed for ν = 0.01 and hmax = 0.01.

Fig. 4. The wave-speed on the bifurcating branch.

Table 1 Numerical values of the control parameters.

Fig. 2. The wave profile.

Citations

Book Chapter•10.1007/978-3-540-28396-6_1

Fluid Flows and Free Boundaries

Ben Schweizer, +3 more

- 01 Jan 2007

TL;DR: In this article, the authors give an overview over results concerning viscous fluids with a free boundary, modelling e.g. the motion of water with a water-air interface.

...read moreread less

References

•Book

The Hopf Bifurcation and Its Applications

Jerrold E. Marsden, +3 more

- 17 Aug 1976

TL;DR: The Hopf bifurcation refers to the development of periodic orbits ("self-oscillations") from a stable fixed point, as a parameter crosses a critical value as mentioned in this paper.

...read moreread less

2.3K

Book•10.1007/BFB0063447

Finite element approximation of the Navier-Stokes equations

Vivette Girault, +1 more

- 01 Jan 1979

TL;DR: A mixed finite element method for solving the stokes problem and the time-dependent navier-stokes equations are presented.

...read moreread less

1.3K

Journal Article•10.1017/S0022112072000783

Microscale pressure fluctuations near waves being generated by the wind

J. A. Elliott

- 08 Aug 1972

- Journal of Fluid Mechanics

TL;DR: In this paper, a large hump in the pressure spectra is observed at the wave frequencies and the amplitude of this hump increases and the rate of its vertical decay decreases as the mean wind speed increases.

...read moreread less

Journal Article•10.1017/S0022112095003818

Parasitic capillary waves: a direct calculation

Michael S. Longuet-Higgins

- 25 Oct 1995

- Journal of Fluid Mechanics

TL;DR: In this article, the authors improved the theory by making use of our more accurate knowledge of the profile of a steep Stokes wave and taking account of the influence of gravity on the capillary waves themselves, through the effective gravitational acceleration g* for short waves riding on longer waves.

...read moreread less

•Book

Lehrbuch der Hydrodynamik

Horace Lamb, +1 more

- 01 Jan 1907

Bifurcation Analysis for Surface Waves Generated by Wind

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Most frequently asked questions

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Citations

Fluid Flows and Free Boundaries

References

The Hopf Bifurcation and Its Applications

Finite element approximation of the Navier-Stokes equations

Microscale pressure fluctuations near waves being generated by the wind

Parasitic capillary waves: a direct calculation

Lehrbuch der Hydrodynamik

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