The free-surface signature of unsteady, two-dimensional vortex flows

Yu, Dequan; Tryggvason, Grétar

doi:10.1017/s0022112090001112

Cited by 41 publications

(26 citation statements)

References 27 publications

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“…This also creates a shear instability between the climbing liquid from the pool and the drop liquid moving down, forming a row of vortex rings of the same sign. These vortices near the free surface leave their signature [29] by creating waves below the rising sheet, a feature also observed experimentally (Fig. 1) [7].…”

supporting

confidence: 72%

von Kármán Vortex Street within an Impacting Drop

et al. 2012

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The splashing of a drop impacting onto a liquid pool produces a range of different sized microdroplets. At high impact velocities, the most significant source of these droplets is a thin liquid jet emerging at the start of the impact from the neck that connects the drop to the pool. We use ultrahigh-speed video imaging in combination with high-resolution numerical simulations to show how this ejecta gives way to irregular splashing. At higher Reynolds numbers, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von Kármán vortex street, thus breaking the ejecta sheet as it forms.

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supporting

confidence: 72%

von Kármán Vortex Street within an Impacting Drop

et al. 2012

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“…f σ is the mean standard deviation of the free surface elevation (average across all longitudinal probes). g k 0 is the characteristic wavenumber estimated according to Equation (9). h n is the exponent of the power-function velocity profile estimated according to Cheng,24 Equations (34) and (35), with n −1  f = 1.0.…”

Section: Flow Conditionsmentioning

confidence: 99%

“…The choice of these parameters for the normalization derived from hypothesis (iii) that the typical spatial scale of the free surface patterns is governed by the interaction with the static rough bed, which produces the stationary waves with the wavenumber k 0 . 2π/k 0 is the wavelength of the stationary waves which were found from the solution of Equation (9). In condition 1, k 0 could not be defined; therefore, the non-dimensionalization for this condition was based on the quantities g/U 0 and 2πU 2 0 /g.…”

Section: A the Spatial And Temporal Scalesmentioning

confidence: 99%

“…These patterns have been studied both experimentally 7,8 and numerically. 9,10 In shallow open channel turbulent flows the effect of gravity is dominating, but the turbulence can effectively disturb the free surface to the point of breaking. 6 The correlation between the free surface elevation and the flow vorticity or turbulent velocities is high in numerical simulations, 10 but generally much lower in experiments, 11,12 where it is difficult to obtain high quality data near the surface, and dispersive waves can affect the correlation locally.…”

Section: Introductionmentioning

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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“…On the other hand, the potential of the whole charge distribution (as opposed to that of each individual charge) is often smooth over the whole region of interest. Therefore, it is possible and often desirable to have simple and efficient interpolation algorithms when a function is to be interpolated from a curve in the plane to the region bounded by that curve, such as in the evaluation of electrostatic or magnetostatic field near a boundary, or the velocity field near a vortex sheet in fluid mechanics (see [2,7,9,20,24]). …”

Section: Introductionmentioning

confidence: 99%