Surface waves on shear currents: solution of the boundary-value problem

Shrira, Victor I.

doi:10.1017/s002211209300388x

Cited by 64 publications

(92 citation statements)

References 9 publications

(11 reference statements)

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“…16,17,19,39 The numerical solution proposed by Shrira 19 applies to an arbitrary shape of the velocity profile, but it has been determined for the infinite depth case only, while the solution derived by Patil and Singh 39 is valid for the logarithmic profile and for the long wavelength limit. The vertical velocity profile in a turbulent shallow flow with rough static bed can be approximated by a power law of the vertical coordinate (Equation (1)), such as the 1/7 power function considered by Fenton 17 and by Lighthill in the Appendix of the work of Burns.…”

Section: Dispersion Relation Of Gravity-capillary Waves On a Shalmentioning

confidence: 99%

“…16,17 The flow rotationality can also promote the growth of resonant waves. The resonant growth of freely propagating gravity waves in a sheared flow has been studied both as the result of the (laminar) critical layer instability 18,19 and of the interaction with turbulent pressure fluctuations. 20 Teixeira and Belcher 20 also described the growth of non-resonant forced waves, which do not satisfy the dispersion relation of gravity-capillary waves but have the same velocity of the pressure turbulence perturbation.…”

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confidence: 99%

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Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

et al. 2016

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Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary Data on the frequency-wavenumber spectra and dispersion relation of the dynamic water surface in an open channel flow are very scarce. In this work, new data on the frequency-wavenumber spectra were obtained in a rectangular laboratory flume with a rough bottom boundary, over a range of subcritical Froude numbers. These data were used to study the dispersion relation of the surface waves in such shallow turbulent water flows. The results show a complex pattern of surface waves, with a range of scales and velocities. When the mean surface velocity is faster than the minimum phase velocity of gravity-capillary waves, the wave pattern is dominated by stationary waves that interact with the static rough bed. There is a coherent three-dimensional pattern of radially propagating waves with the wavelength approximately equal to the wavelength of the stationary waves. Alongside these waves, there are freely propagating gravity-capillary waves that propagate mainly parallel to the mean flow, both upstream and downstream. In the flow conditions where the mean surface velocity is slower than the minimum phase velocity of gravitycapillary waves, patterns of non-dispersive waves are observed. It is suggested that these waves are forced by turbulence. The results demonstrate that the free surface carries information about the underlying turbulent flow. The knowledge obtained in this study paves the way for the development of novel airborne methods of non-invasive flow monitoring. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Section: Dispersion Relation Of Gravity-capillary Waves On a Shalmentioning

confidence: 99%

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confidence: 99%

Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

et al. 2016

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“…(18) relates to the vortex mode perturbation [11,13], whereas the second term, which is exponentially decreasing with the depth, relates to the SFHs of shear modified surface waves.…”

Section: Mathematical Formalismmentioning

confidence: 99%

Surface gravity waves in deep fluid at vertical shear flows

Gogoberidze

Samushia²,

Chagelishvili³

et al. 2005

J. Exp. Theor. Phys.

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Special features of surface gravity waves in deep fluid flow with constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to non-trivial modification of surface gravity wave modes dispersive characteristics. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study provides, that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. Generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the later wave is generated more effectively for the high shear rates. From the mathematical point of view the wave generation is caused by non self-adjointness of the linear operators that describe the shear flow.

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“…Many studies and models in these areas have used simple velocity profiles such as depth-uniform or linear depth dependence, largely due to mathematical tractability as analytical solutions exist only for a select few of these current profiles 1 . Various approximation techniques have been developed for more realistic profiles 2,[6][7][8][9] , yet these have limited range of applicability. The goal of this work is to demonstrate an approximation method for calculating the dispersion relation on an arbitrary current profile in three dimensions valid for all wavelengths that is suitable for practical calculations by engineers.…”

Section: Introductionmentioning

confidence: 99%

“…To treat profiles with arbitrary current depth-dependence, various approximation techniques have been developed, typically involving expansions in a small parameter representing the magnitude of the current velocity relative to the phase velocity of the waves 2,6-8 , or the departure from a velocity potential solution 9 . These methods have been used for many practical calculations such as inferring the background current from phase velocity measurements [2][3][4][5] , yet complications occur when applying them to problems involving the entire wave-spectrum as their accuracy is difficult to predict a priori and can suffer in certain wavelength regimes.…”

Section: Introductionmentioning

confidence: 99%

Surface waves on currents with arbitrary vertical shear

Smeltzer

Ellingsen

2017

Physics of Fluids

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We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for practical calculation. The method has been much used in the past for the case of waves propagating along the same axis as the background current, and we herein extend and apply it to problems with an arbitrary angle between the wave propagation and current directions. Being valid for all wavelengths without loss of accuracy, the scheme is particularly well suited to solve problems involving a broad range of wave vectors, such as ship waves and Cauchy-Poisson initial value problems for example. We examine the group and phase velocities over different wavelength regimes and current profiles, highlighting characteristics due to the depth-variable vorticity. We show an example application to ship waves on an arbitrary current profile, and demonstrate qualitative differences in the wake patterns between concave down and concave up profiles when compared to a constant shear profile with equal depth-averaged vorticity. We also discuss the nature of additional solutions to the dispersion relation when using the piecewise-linear model. These are vorticity waves, drifting vortical structures which are artifacts of the piecewise model. They are absent for a smooth profile and are spurious in the present context.

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Surface waves on shear currents: solution of the boundary-value problem

Cited by 64 publications

References 9 publications

Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

Surface gravity waves in deep fluid at vertical shear flows

Surface waves on currents with arbitrary vertical shear

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