3 results
Air entrapment at impact of a conus onto a liquid
- J.-B. Carrat, N. Gavrilov, A. Cherdantsev, N. Shmakova, E. Ermanyuk
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- Journal:
- Journal of Fluid Mechanics / Volume 966 / 10 July 2023
- Published online by Cambridge University Press:
- 03 July 2023, R1
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In this experimental work, a conus impacts a deep liquid pool at a speed varying from 1.3 to $19.0\ {\rm cm}\ {\rm s}^{-1}$. Two liquids (2.5 % butanol–water solution or distilled water) and four coni made from duralumin with a diameter of 180 mm and different deadrise angles $\beta$ ($2^{\circ }$, $3^{\circ }$, $4^{\circ }$ and 5$^{\circ }$) are tested. An air cushion is trapped between the conus solid surface and the liquid. Several types of bubble patterns after the collapse of the air cushion are observed: one or multiple bubbles near the conus centre (vertex), irregular trails of bubbles on the conus surface and a ring of bubbles in a ‘necklace’-shaped arrangement. With a total internal reflection set-up and appropriate image post-processing, the external and internal radii of the ring-shaped wetted area are estimated for each frame. The external (internal) radius increases (decreases) in time following a linear (exponential) law. The speed of the outer border of the wetted area is in agreement with the Wagner theory for a body impacting onto a liquid. The initial radius of the annular touchdown region is estimated as the intersection of the relevant fitting curves. In the studied range of parameters, the initial radius obeys a universal scaling law, which follows from the air–water lubrication–inertia balance.
Vortex cluster arising from an axisymmetric inertial wave attractor
- S. Boury, I. Sibgatullin, E. Ermanyuk, N. Shmakova, P. Odier, S. Joubaud, L.R.M. Maas, T. Dauxois
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- Journal:
- Journal of Fluid Mechanics / Volume 926 / 10 November 2021
- Published online by Cambridge University Press:
- 06 September 2021, A12
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We present an experimental and numerical study of the nonlinear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The rotating ring-shaped fluid domain is delimited by two vertical coaxial cylinders, a conical bottom and a horizontal wave generator at the top: the vertical cross-section is a trapezium, while the horizontal cross-section is a ring. Forcing is introduced via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. The experiment shows an important result: at sufficiently strong forcing and long time scale, a saturated fully nonlinear regime develops as a consequence of an energy transfer draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially oriented cyclonic vortices undergoing a slow prograde motion around the inner cylinder. We explore the long-term nonlinear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. This study shows a rich variety of dynamical regimes, including a linear behaviour, a triadic resonance instability, a progressive frequency enrichment reminiscent of weak inertial wave turbulence and the generation of a slow manifold in the form of a polygonal vortex cluster confirming the experimental observation. This vortex cluster is discussed in detail, and we show that it stems from the summation and merging of wave-like components of the vorticity field. The nature of these wave components, the possibility of their detection under general conditions and the ultimate fate of the vortex clusters at even longer time scale remain to be explored.
Internal wave focusing by a horizontally oscillating torus
- E. V. Ermanyuk, N. D. Shmakova, J.-B. Flór
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- Journal:
- Journal of Fluid Mechanics / Volume 813 / 25 February 2017
- Published online by Cambridge University Press:
- 26 January 2017, pp. 695-715
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This paper presents an experimental study on internal waves emitted by a horizontally oscillating torus in a linearly stratified fluid. Two internal wave cones are generated with the kinetic energy focused at the apices of the cones above and below the torus where the wave amplitude is maximal. Their motion is measured via tracking of distortions of horizontal fluorescein dye planes created prior to the experiments and illuminated by a vertical laser sheet. The distortion of the dye planes gives a direct access to the Lagrangian displacement of local wave amplitudes and slopes, and in particular, allows us to calculate a local Richardson number. In addition particle image velocimetry measurements are used. Maximum wave slopes are found in the focal region and close to the surface of the torus. As the amplitude of oscillations of the torus increases, wave profiles in the regions of maximum wave slopes evolve nonlinearly toward local overturning. A theoretical approximation based on the theory of Hurley & Keady (J. Fluid Mech., vol. 351, 1997, pp. 119–138) is presented and shows, for small amplitudes of oscillation, a very reasonable agreement with the experimental data. For the focal region the internal wave amplitude is found to be overestimated by the theory. The wave breaking in the focal region is investigated as a function of the Keulegan–Carpenter number, $Ke=A/a$, with $A$ the oscillation amplitude and $a$ the short radius of the torus. A linear wave regime is found for $Ke<0.4$, nonlinear effects start at $Ke\approx 0.6$ and breaking for $Ke>0.8$. For large forcing, the measured wave amplitude normalized with the oscillation amplitude decreases almost everywhere in the wave field, but increases locally in the focal region due to nonlinear effects. Due to geometric focusing the amplitude of the wave increases with $\sqrt{\unicode[STIX]{x1D716}}$, with $\unicode[STIX]{x1D716}=b/a$ and $b$ is the mean radius of the torus. The relevance of wave focusing due to ocean topography is discussed.