7 results
Hysteresis phenomena in gravity–capillary waves on deep water generated by a moving two-dimensional/three-dimensional air-blowing/air-suction forcing
- Beomchan Park, Yeunwoo Cho
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- Journal:
- Journal of Fluid Mechanics / Volume 885 / 25 February 2020
- Published online by Cambridge University Press:
- 23 December 2019, A20
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Hysteresis phenomena in forced gravity–capillary waves on deep water where the minimum phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$ are experimentally investigated. Four kinds of forcings are considered: two-dimensional/three-dimensional air-blowing/air-suction forcings. For a still-water initial condition, as the forcing speed increases from zero towards a certain target speed ($U$), there exists a certain critical speed ($U_{crit}$) at which the transition from linear to nonlinear states occurs. When $U<U_{crit}$, steady linear localized waves are observed (state I). When $U_{crit}<U<c_{min}$, steady nonlinear localized waves, including steep gravity–capillary solitary waves, are observed (state II). When $U\approx c_{min}$, periodic shedding phenomena of nonlinear localized depressions are observed (state III). When $U>c_{min}$, steady linear non-local waves are observed (state IV). Next, with these state-II, III and IV waves as new initial conditions, as the forcing speed is decreased towards a certain target speed ($U_{final}$), a certain critical speed ($U_{crit,2}$) is identified at which the transition from nonlinear to linear states occurs. When $U_{crit,2}<U_{final}<U_{crit}$, relatively steeper steady nonlinear localized waves, including steeper gravity–capillary solitary waves, are observed. When $U_{final}<U_{crit,2}$, linear state-I waves are observed. These are hysteresis phenomena, which show jump transitions from linear to nonlinear states and from nonlinear to linear states at two different critical speeds. For air-blowing cases, experimental results are compared with simulation results based on a theoretical model equation. They agree with each other very well except that the experimentally identified critical speed ($U_{crit,2}$) is different from the theoretically predicted one.
Gravity–capillary jet-like surface waves generated by an underwater bubble
- Youn J. Kang, Yeunwoo Cho
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- Journal:
- Journal of Fluid Mechanics / Volume 866 / 10 May 2019
- Published online by Cambridge University Press:
- 18 March 2019, pp. 841-864
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Jet-like surface waves generated by an electric-spark-generated underwater bubble are experimentally studied. Three different motions of jet-like surface waves are observed depending on the inception position of the bubble ($d$: 0.28–7 mm) below the free surface and the maximum radius of the bubble ($R_{m}$: 1.5–3.6 mm). When $d/R_{m}>1.3$, the surface wave shows a simple smooth hump (case 1). When $0.82<d/R_{m}<1.3$, a single droplet or multiple droplets are pinched off sequentially or simultaneously at the tip or from some points of the jet-like surface wave (case 2). Finally, when $d/R_{m}<0.82$, a series of squirting and jetting phenomena are observed at the top of the jet-like surface wave (case 3). For case 1, a proportional relationship is found between $\unicode[STIX]{x1D70C}gh/\unicode[STIX]{x0394}p$ and $(d/R_{m})^{-4.4}$, where $\unicode[STIX]{x1D70C}$ is the density of the fluid, $g$ is the gravitational acceleration and $\unicode[STIX]{x0394}p$ is the difference between the reference atmospheric pressure and the vapour pressure inside a bubble. This proportional relationship is explained semi-analytically using a scaling argument and conservation of momentum and energy, with the help of the Kelvin impulse theory. In addition, we solve the relevant axisymmetric Cauchy–Poisson problem where the initial condition is a jet-like surface wave near its maximum height. By comparing the analytical wave solution with the observed surface wave pattern, it is found that the resultant surface waves are indeed gravity–capillary waves where both the gravity and the surface tension are equally important.
Ventilated supercavitation around a moving body in a still fluid: observation and drag measurement
- Jaeho Chung, Yeunwoo Cho
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- Journal:
- Journal of Fluid Mechanics / Volume 854 / 10 November 2018
- Published online by Cambridge University Press:
- 06 September 2018, pp. 367-419
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This experimental study examines ventilated supercavity formation in a free-surface bounded environment where a body is in motion and the fluid is at rest. For a given torpedo-shaped body and water depth ($H$), depending on the cavitator diameter ($d_{c}$) and the submergence depth ($h_{s}$), four different cases are investigated according to the blockage ratio ($B=d_{c}/d_{h}$, where $d_{h}$ is the hydraulic diameter) and the dimensionless submergence depth ($h^{\ast }=h_{s}/H$). Cases 1–4 are, respectively, no cavitator in fully submerged ($B=0$, $h^{\ast }=0.5$), small blockage in fully submerged ($B=1.5\,\%$, $h^{\ast }=0.5$), small blockage in shallowly submerged ($B=1.5\,\%$, $h^{\ast }=0.17$) and large blockage in fully submerged ($B=3\,\%$, $h^{\ast }=0.5$) cases. In case 1, no supercavitation is observed and only a bubbly flow (B) and a foamy cavity (FC) are observed. In non-zero blockage cases 2–4, various non-bubbly and non-foamy steady states are observed according to the cavitator-diameter-based Froude number ($Fr$), air-entrainment coefficient ($C_{q}$) and the cavitation number ($\unicode[STIX]{x1D70E}_{c}$). The ranges of $Fr$, $C_{q}$ and $\unicode[STIX]{x1D70E}_{c}$ are $Fr=2.6{-}18.2$, $C_{q}=0{-}6$, $\unicode[STIX]{x1D70E}_{c}=0{-}1$ for cases 2 and 3, and $Fr=1.8{-}12.9$, $C_{q}=0{-}1.5$, $\unicode[STIX]{x1D70E}_{c}=0{-}1$ for case 4. In cases 2 and 3, a twin-vortex supercavity (TV), a reentrant-jet supercavity (RJ), a half-supercavity with foamy cavity downstream (HSF), B and FC are observed. Supercavities in case 3 are not top–bottom symmetric. In case 4, a half-supercavity with a ring-type vortex shedding downstream (HSV), double-layer supercavities (RJ inside and TV outside (RJTV), TV inside and TV outside (TVTV), RJ inside and RJ outside (RJRJ)), B, FC and TV are observed. The cavitation numbers ($\unicode[STIX]{x1D70E}_{c}$) are approximately 0.9 for the B, FC and HSF, 0.25 for the HSV, and 0.1 for the TV, RJ, RJTV, TVTV and RJRJ supercavities. In cases 2–4, for a given $Fr$, there exists a minimum cavitation number in the formation of a supercavity while the minimum cavitation number decreases as the $Fr$ increases. In cases 2 and 3, it is observed that a high $Fr$ favours an RJ and a low $Fr$ favours a TV. For the RJ supercavities in cases 2 and 3, the cavity width is always larger than the cavity height. In addition, the cavity length, height and width all increase (decrease) as the $\unicode[STIX]{x1D70E}_{c}$ decreases (increases). The cavity length in case 3 is smaller than that in case 2. In both cases 2 and 3, the cavity length depends little on the $Fr$. In case 2, the cavity height and width increase as the $Fr$ increases. In case 3, the cavity height and width show a weak dependence on the $Fr$. Compared to case 2, for the same $Fr$, $C_{q}$ and $\unicode[STIX]{x1D70E}_{c}$, case 4 admits a double-layer supercavity instead of a single-layer supercavity. Connected with this behavioural observation, the body-frontal-area-based drag coefficient for a moving torpedo-shaped body with a supercavity is measured to be approximately 0.11 while that for a cavitator-free moving body without a supercavity is approximately 0.4.
Two-dimensional gravity–capillary solitary waves on deep water: generation and transverse instability
- Beomchan Park, Yeunwoo Cho
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- Journal:
- Journal of Fluid Mechanics / Volume 834 / 10 January 2018
- Published online by Cambridge University Press:
- 17 November 2017, pp. 92-124
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Two-dimensional (2-D) gravity–capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of the deep water at speeds close to the minimum phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Four different states are observed according to the forcing speed. At relatively low speeds below $c_{min}$, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{min}$, nonlinear 2-D gravity–capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{min}$, periodic shedding of a 2-D local depression is observed behind the moving forcing. Finally, at relatively high speeds above $c_{min}$, a pair of short and long linear waves is observed, respectively ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity–capillary solitary waves and, further, the resultant formation of three-dimensional gravity–capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity–capillary solitary wave solutions near $c_{min}$. They agree with each other very well. In particular, based on a linear stability analysis, we give a theoretical proof for the transverse instability of the 2-D gravity–capillary solitary waves on deep water.
Experimental observation of gravity–capillary solitary waves generated by a moving air suction
- Beomchan Park, Yeunwoo Cho
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- Journal:
- Journal of Fluid Mechanics / Volume 808 / 10 December 2016
- Published online by Cambridge University Press:
- 27 October 2016, pp. 168-188
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Gravity–capillary solitary waves are generated by a moving ‘air-suction’ forcing instead of a moving ‘air-blowing’ forcing. The air-suction forcing moves horizontally over the surface of deep water with speeds close to the minimum linear phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Three different states are observed according to forcing speeds below $c_{min}$. At relatively low speeds below $c_{min}$, small-amplitude linear circular depressions are observed, and they move steadily ahead of and along with the moving forcing. As the forcing speed increases close to $c_{min}$, however, nonlinear three-dimensional (3-D) gravity–capillary solitary waves are observed, and they move steadily ahead of and along with the moving forcing. Finally, when the forcing speed is very close to $c_{min}$, oblique shedding phenomena of 3-D gravity–capillary solitary waves are observed ahead of the moving forcing. We found that all the linear and nonlinear wave patterns generated by the air-suction forcing correspond to those generated by the air-blowing forcing. The main difference is that 3-D gravity–capillary solitary waves are observed ‘ahead of’ the air-suction forcing whereas the same waves are observed ‘behind’ the air-blowing forcing.
Resonantly forced gravity–capillary lumps on deep water. Part 2. Theoretical model
- YEUNWOO CHO, JAMES D. DIORIO, T. R. AKYLAS, JAMES H. DUNCAN
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- Journal:
- Journal of Fluid Mechanics / Volume 672 / 10 April 2011
- Published online by Cambridge University Press:
- 31 March 2011, pp. 288-306
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A theoretical model is presented for the generation of waves by a localized pressure distribution moving on the surface of deep water with speed near the minimum gravity–capillary phase speed, cmin. The model employs a simple forced–damped nonlinear dispersive equation. Even though it is not formally derived from the full governing equations, the proposed model equation combines the main effects controlling the response and captures the salient features of the experimental results reported in Diorio et al. (J. Fluid Mech., vol. 672, 2011, pp. 268–287 – Part 1 of this work). Specifically, as the speed of the pressure disturbance is increased towards cmin, three distinct responses arise: state I is confined beneath the applied pressure and corresponds to the linear subcritical steady solution; state II is steady, too, but features a steep gravity–capillary lump downstream of the pressure source; and state III is time-periodic, involving continuous shedding of lumps downstream. The transitions from states I to II and from states II to III, observed experimentally, are associated with certain limit points in the steady-state response diagram computed via numerical continuation. Moreover, within the speed range that state II is reached, the maximum response amplitude turns out to be virtually independent of the strength of the pressure disturbance, in agreement with the experiment. The proposed model equation, while ad hoc, brings out the delicate interplay between dispersive, nonlinear and viscous effects that takes place near cmin, and may also prove useful in other physical settings where a phase-speed minimum at non-zero wavenumber occurs.
Resonantly forced gravity–capillary lumps on deep water. Part 1. Experiments
- JAMES D. DIORIO, YEUNWOO CHO, JAMES H. DUNCAN, T. R. AKYLAS
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- Journal:
- Journal of Fluid Mechanics / Volume 672 / 10 April 2011
- Published online by Cambridge University Press:
- 31 March 2011, pp. 268-287
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The wave pattern generated by a pressure source moving over the free surface of deep water at speeds, U, below the minimum phase speed for linear gravity–capillary waves, cmin, was investigated experimentally using a combination of photographic measurement techniques. In similar experiments, using a single pressure amplitude, Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) pointed out that the resulting surface response pattern exhibits remarkable nonlinear features as U approaches cmin, and three distinct response states were identified. Here, we present a set of measurements for four surface-pressure amplitudes and provide a detailed quantitative examination of the various behaviours. At low speeds, the pattern resembles the stationary state (U = 0), essentially a circular dimple located directly under the pressure source (called a state I response). At a critical speed, but still below cmin, there is an abrupt transition to a wave-like state (state II) that features a marked increase in the response amplitude and the formation of a localized solitary depression downstream of the pressure source. This solitary depression is steady, elongated in the cross-stream relative to the streamwise direction, and resembles freely propagating gravity–capillary ‘lump’ solutions of potential flow theory on deep water. Detailed measurements of the shape of this depression are presented and compared with computed lump profiles from the literature. The amplitude of the solitary depression decreases with increasing U (another known feature of lumps) and is independent of the surface pressure magnitude. The speed at which the transition from states I to II occurs decreases with increasing surface pressure. For speeds very close to the transition point, time-dependent oscillations are observed and their dependence on speed and pressure magnitude are reported. As the speed approaches cmin, a second transition is observed. Here, the steady solitary depression gives way to an unsteady state (state III), characterized by periodic shedding of lump-like disturbances from the tails of a V-shaped pattern.