Water-wave instability induced by a drift layer

Caponi, Enrique A.; Yuen, Henry C.; Milinazzo, F.; Saffman, P. G.

doi:10.1017/s0022112091001064

Cited by 29 publications

(19 citation statements)

References 1 publication

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“…Comparison of figure 2 with figure 3 shows that the result of reducing the surface speed U s from 2c min to c min /2, while holding all other parameters fixed, is to eliminate the rippling instability. This elimination illustrates a main conclusion of Caponi et al (1991): activation of the rippling instability requires…”

Section: The Unstable Modesmentioning

confidence: 61%

Generation of surface waves by shear-flow instability

Young

Wolfe

2013

J. Fluid Mech.

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We consider the linear stability of an inviscid parallel shear flow of air over water with gravity and capillarity. The velocity profile in the air is monotonically increasing upwards from the sea surface and is convex, while the velocity in the water is monotonically decreasing from the surface and is concave. An archetypical example, the ‘double-exponential’ profile, is solved analytically and studied in detail. We show that there are two types of unstable mode which can, in some cases, co-exist. The first type is the ‘Miles mode’ resulting from a resonant interaction between a surface gravity wave and a critical level in the air. The second unstable mode is an interaction between surface gravity waves and a critical level in the water, resulting in the growth of ripples. The gravity–capillary waves participating in this second resonance have negative intrinsic phase speed, but are Doppler shifted so that their actual phase speed is positive, and matches the speed of the base-state current at the critical level. In both cases, the Reynolds stresses of an exponentially growing wave transfer momentum from the vicinity of the critical level to the zone between the crests and troughs of a surface wave.

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Section: The Unstable Modesmentioning

confidence: 61%

Generation of surface waves by shear-flow instability

Young

Wolfe

2013

J. Fluid Mech.

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“…A quasisteady wave-current flow therefore could be achieved where the characteristics of wave-current interaction are primarily dependent on the vertical current shear. 6,30 To avoid wave instability induced by a surface drift layer, 7,31 very strong vertical shear was not attempted here. In the absence of waves, the maximum surface disturbance of the fast current was less than 0.5 mm.…”

Section: B Generation Of Sheared Currentsmentioning

confidence: 99%

Incipient breaking of unsteady waves on sheared currents

Yao

2005

Physics of Fluids

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Incipient breaking of unsteady waves on sheared currents is experimentally investigated. A new wave-generation technique, based on the iterative frequency-focusing concept with the consideration of effects of Doppler shift and current shear, is developed. The surface displacement, the wavelength, and the phase speed of waves at the breaking onset on shear currents are measured. It is found that the steepness of unsteady, incipient breaking waves is altered by the sign and magnitude of current shear ͑or vorticity͒. A current with a positive shear, as would be the case in a wind-driven current, reduces the steepness of an unsteady incipient breaking wave. A negatively sheared current, such as the jet-like ebb current at a tide inlet, leads to steeper incipient breaking waves. The magnitude of reduction/increase in wave steepness is proportional to the strength of a current shear. In particular, a negative shear can alter the wave steepness more significantly in comparison to a positive shear of the same magnitude. Interestingly, the trend of crest-trough asymmetry with respect to the change of a current shear is in contrast to the limiting wave steepness. A positively sheared current can dramatically increase crest-trough asymmetry for unsteady waves. Dimensionless amplitudes of unsteady waves at incipient breaking are well correlated with surface current drifts. Positive/negative surface drifts lead to the reduced/increased dimensionless wave amplitudes. However, the change in dimensionless wave amplitude of unsteady waves is much smaller than that of steady waves.

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“…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%

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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Water-wave instability induced by a drift layer

Cited by 29 publications

References 1 publication

Generation of surface waves by shear-flow instability

Generation of surface waves by shear-flow instability

Incipient breaking of unsteady waves on sheared currents

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

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